Search

In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective modules). We show that they behave in a way similar to the classical ones. As an application, we characterize ϕ-rings over which every NN-torsion-free module is NN-injective. [ABSTRACT FROM AUTHOR]

In the present paper we shall obtain the following result: Let n ≥ 2 and m ≥ 1 be integers. Let p (x 1 , ... , x m) be a polynomial with zero constant term in non-commutative variables over an algebraically closed field K. Suppose that 1 ≤ r ≤ n − 1 , where r is the order of p. Then p (T n (K)) is a dense subset of T n (K) (r − 1) (with respect to the Zariski topology). This is a solution of a problem presented by Gargate and de Mello and a supplement to a result obtained by Panja and Prasad in 2023. [ABSTRACT FROM AUTHOR]

In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a characterization of prime partial skew groupoid rings, and in particular of prime groupoid rings, thereby generalizing a classical result by Connell and partially generalizing recent results by Steinberg. [ABSTRACT FROM AUTHOR]

In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given. [ABSTRACT FROM AUTHOR]

The Beckmann-Black problem asks whether any given finite Galois extension E/K of group G is the specialization at some point t 0 ∈ P 1 (K) of some finite regular Galois extension F / K (T) with the same group. In this paper, we study a generalization of this problem for infinite extensions, via the profinite twisting lemma, and apply the latter in many situations, like abelian infinite extensions and the l -universal Frattini cover of an arbitrary finite group. [ABSTRACT FROM AUTHOR]

We study the rings Nil D of nilpotent elements of R-derivations D on polynomial rings over a UFD R containing Q . The main result of this paper determines Nil D of the monomial derivations D on R [ x , y ] . Furthermore, as its application, we prove that, for each positive integer m, there exists a monomial R-derivation with a slice on R [ x , y , z ] such that the minimal number of generators of its kernel equals m. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

We compute the wonderful compactification of symmetric varieties of SL (2 , F) , where F is a finite field-extension of Q p with p ≠ 2 , that comes from either an abstract or an F -involution of SL (2 , F) . For each of those wonderful compactifications we find the SL (2 , F) -stabilizers of the accumulation points of the corresponding symmetric varieties and show they agree with the Chabauty limits found in an earlier paper by the author and Arielle Leitner from 2023. [ABSTRACT FROM AUTHOR]

Which groups can occur as the group of units in a ring? Such groups are called realizable. Though the realizable members of several classes of groups have been determined (e.g., cyclic, odd order, alternating, symmetric, finite simple, indecomposable abelian, and dihedral), the question remains open. The general linear groups are realizable by definition: they are the units in the corresponding matrix rings. In this paper, we study the realizability of two closely related linear groups, the special linear groups and the affine general linear groups. We determine which special linear groups of degree 2 over a finite field are realizable by a finite ring, and we determine which affine general linear groups of degree 1 over a cyclic group are realizable by a finite ring. We also give partial results for certain linear groups of other degrees and for rings of characteristic zero. [ABSTRACT FROM AUTHOR]

A ring extension is a ring homomorphism preserving identities. In this paper, we give the definitions of relative injective envelopes and relative projective covers of modules on ring extensions, and study their basic properties. In particular, we give their equivalent characterizations in terms of relative essential monomorphisms and relative superfluous epimorphisms, and prove that relative injective envelopes and relative projective covers on ring extensions are unique up to isomorphism whenever they exist. Moreover, for an extension of Artin algebras, we show that every finitely generated module has both a relative injective envelope and a relative projective cover. In addition, we compare relative injective envelopes and relative projective covers on two ring extensions linked by surjective homomorphisms of rings respectively. [ABSTRACT FROM AUTHOR]

Let K be an algebraically closed characteristic 0 field and let V be the K-vector space with basis { x 0 , x 1 , x 2 , ... } . In this paper we use the theory developed in [17] to associate with each power series f ∈ K [ [ X ] ] satisfying f (0) = 1 , an involutive solution s (f) : V ⊗ V → V ⊗ V , of the braid equation, and we begin the study of this correspondence. For n ≥ 2 , let Vn be the subspace of V generated by { x 0 , ... , x n − 1 } . Each one of the solution s(f) induces by restriction a solution s n (f) on V n ⊗ V n . We also begin the study of these solutions. [ABSTRACT FROM AUTHOR]

In characteristic 0, the Campana-Peternell conjecture claims that the only smooth Fano variety with nef tangent bundle should be homogeneous. In this paper, we study the positive characteristic version of the Campana-Peternell conjecture. In particular, we give an affirmative answer for Fano 4-folds with nef tangent bundle and Picard number greater than one. [ABSTRACT FROM AUTHOR]

Extriangulated categories were introduced by Nakaoka and Palu, which is a simultaneous generalization of exact categories and triangulated categories. Axiom (ET4) for extriangulated categories is an analogue of octahedron axiom (TR4) for triangulated categories. In this paper, we use homotopy cartesian squares in pre-extriangulated categories to investigate axiom (ET4). We provide several equivalent statements of axiom (ET4) and find out conditions under which the axiom is self-dual. [ABSTRACT FROM AUTHOR]

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime p, we prove a sufficient condition for a finite group to be p-nilpotent, that is, a group whose elements of p ′ -order form a normal subgroup. Moreover, we characterize finite cyclic groups with prescribed number of prime divisors. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

As a proper generalization of comultiplication modules, the concept of k-comultipli-cation semimodules is introduced in this paper. Let S be a semiring. An left S-semimodule M is called a left k-comultiplication semimodule if for each subtractive subsemimodule N of M, there exists an ideal I of S such that N = (0 : M r I) . Some properties of k-comultiplication semimodules are obtained and some conditions are given for a direct sum of k-comultiplication semimodules to be a k-comultiplication semimodule. [ABSTRACT FROM AUTHOR]

We show that any n-absorbing ideal must be strongly n-absorbing, which is the first of Anderson and Badawi's three interconnected conjectures on absorbing ideals. We prove this by introducing and studying objects called maximal and semimaximal collections, which are tools for analyzing the multiplicative ideal structure of commutative rings. Furthermore, we discuss and make heavy use of previous work on absorbing ideals done by Anderson and Badawi, Choi and Walker, Laradji, and Donadze, among others. At the end of this paper, we pose three conjectures, each of which implies the last unsolved conjecture made by Anderson and Badawi. [ABSTRACT FROM AUTHOR]

This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a derivation, and to demonstrate that every local or 2-local automorphism of the super-Virasoro algebras is an automorphism. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic p ≥ 0 , let G be a simple simply connected classical linear algebraic group of rank l and let T be a maximal torus in G with rational character group X (T) . For a nonzero p-restricted dominant weight λ ∈ X (T) , let V be the associated irreducible kG-module. We define ν G (V) as the minimum codimension of any eigenspace on V for any non-central element of G. In this paper, we determine lower-bounds for ν G (V) for G of type A l and dim (V) ≤ l 3 2 , and for G of type B l , C l , or D l and dim (V) ≤ 4 l 3 . Moreover, we give the exact value of ν G (V) for G of type A l with l ≥ 15 ; for G of type B l or C l with l ≥ 14 ; and for G of type D l with l ≥ 16 . [ABSTRACT FROM AUTHOR]

For a commutative ring R and a Hopf algebra H which is finitely generated projective as an R-module, it is established that there is an (anti)-isomorphism of groups between the Brauer group BQ(R, H) of Hopf Yetter-Drinfel'd H-module algebras and the Brauer group BQ (R , H *) of Hopf Yetter-Drinfel'd H * -module algebras, where H * is the linear dual of H. In this paper, we generalize this result by establishing an anti-isomorphism of groups between BQ(S, H), the Brauer group of dyslectic Hopf Yetter-Drinfel'd (S, H)-module algebras and BQ (S o p , H *) , the Brauer group of dyslectic Hopf Yetter-Drinfel'd (S o p , H *) -module algebras, where S is an H-commutative Hopf Yetter-Drinfel'd H-module algebra and Sop is the opposite algebra of S. Communicated by Alberto Elduque [ABSTRACT FROM AUTHOR]

Let I (Γ) be the homogeneous ideal of a finite set Γ in P n of d points in linearly general position. In 1972, Saint-Donat proved that if d ≤ 2 n then I (Γ) is generated by completely decomposable quadratic polynomials. Later, R. Treger generalized this result by showing that I (Γ) is generated by forms of degree ≤ m if d ≤ mn for some m ≥ 2 . This paper aims to generalize Saint-Donat's work in a different direction by proving that the degree m piece of I (Γ) can be generated by completely decomposable forms of degree m if and only if d ≤ mn . Communicated by Daniel Erman [ABSTRACT FROM AUTHOR]

The present paper is devoted to study local derivations on the conformal Galilei algebra. We prove that every local derivation on the conformal Galilei algebra is a derivation. [ABSTRACT FROM AUTHOR]

Given a finite set A and a group homomorphism ϕ : H → G , a ϕ -cellular automaton is a function T : A G → A H that is continuous with respect to the prodiscrete topologies and ϕ -equivariant in the sense that h · T (x) = T (ϕ (h) · x) , for all x ∈ A G , h ∈ H , where · denotes the shift actions of G and H on A G and AH, respectively. When G = H and ϕ = id , the definition of id -cellular automata coincides with the classical definition of cellular automata. The purpose of this paper is to expand the theory of ϕ -cellular automata by focusing on the differences and similarities with their classical counterparts. After discussing some basic results, we introduce the following definition: a ϕ -cellular automaton T : A G → A H has the unique homomorphism property (UHP) if T is not ψ-equivariant for any group homomorphism ψ : H → G , ψ ≠ ϕ . We show that if the difference set Δ (ϕ , ψ) is infinite, then T is not ψ-equivariant; it follows that when G is torsion-free abelian, every non-constant T has the UHP. Furthermore, inspired by the theory of classical cellular automata, we study ϕ -cellular automata over quotient groups, as well as their restriction and induction to subgroups and supergroups, respectively. [ABSTRACT FROM AUTHOR]

In 1971, inspired by the work of Lazard and Govorov for R-modules over a ring R, B. Stenström proved that an S-act over a monoid S is isomorphic to a directed colimit of finitely generated free S-acts if and only if it is both pullback flat and equalizer flat. Such acts are now usually called strongly flat. In 1991, S. Bulman-Fleming discovered that every pullback flat S-act is in fact strongly flat by developing a new "interpolation" Condition (PF) for pullback-preservation. In 2005, V. Laan and S. Bulman-Fleming obtained a version of the Lazard-Govorov Theorem for S-posets over a pomonoid S, in which subpullbacks and subequalizers now take on the role previously played by pullbacks and equalizers. However, unlike the situation for acts, S. Bulman-Fleming showed in 2009 that subpullback flat S-posets need not be strongly flat, and also T. Zhao found in 2022 that Condition (PF) does not imply strongly flatness for S-posets. The present paper is devoted to the study of subpullback flatness and Condition (PF) in the context of S-posets over a pomonoid S. First we unexpectedly show that subpullback flatness is equivalent to Condition (PF). Furthermore, we give some classifications of pomonoids by subpullback flatness of (cyclic, Rees factor) S-posets, and give some classes of pomonoids that all (cyclic) S-posets have a PF-cover. Finally, we investigate products of subpullback flat S-posets. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the structure of groups with the property of the core relation between some second maximal subgroups and corresponding maximal subgroups, and obtained some new results about finite groups. ARTICLE HISTORY Received 7 September 2023 Revised 13 December 2023 Communicated by Mandi Schaeffer Fry [ABSTRACT FROM AUTHOR]

In the paper, we show that a uniformly bounded and nonnegative triangle functor between Gorenstein derived categories of two CM-algebras induces a Gorenstein-projectively stable functor between the corresponding Gorenstein-projectively stable categories. Furthermore, we show that a ladder of Gorenstein derived categories of CM-finite algebras induces a recollement of Gorenstein-projectively stable categories under certain nice conditions. As a byproduct, a Gorenstein derived equivalence induces a Gorenstein-projectively stable equivalence for CM-finite Gorenstein algebras. [ABSTRACT FROM AUTHOR]

Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter algebra was proposed by Guo and Keigher. Recently, the subject has attracted more attention since it is associated with many areas in mathematics, such as integro-differential algebras. This paper considers differential Rota-Baxter algebras in the quasi-idempotent operator context. We establish a Gröbner-Shirshov basis for free commutative quasi-idempotent differential algebras (resp. Rota-Baxter algebras, resp. differential Rota-Baxter algebras). This provides a linear basis of a free object in each of the three corresponding categories by the Composition-Diamond lemma. Communicated by P. Kolesnikov [ABSTRACT FROM AUTHOR]

Let R be a commutative Noetherian ring and M be an R-module. The R-module M is called distributive if for every submodules S, T and U of M, the equality S ∩ (T + U) = S ∩ T + S ∩ U holds true. In this paper, we give a necessary and sufficient condition for M to be distributive based on injective envelopes. The proof uses Matlis' results on injective modules. [ABSTRACT FROM AUTHOR]

In this paper, we unfold balanced and totally balanced neighborhood hypergraphs to discover new classes of normally torsion-free monomial ideals. As a consequence, we establish that the closed neighborhood ideals and the dominating ideals of strongly chordal graphs are normally torsion-free. We discuss the stable sets of associated primes of the dominating ideals of cycles and characterize all the cycles with normally torsion-free dominating ideals. [ABSTRACT FROM AUTHOR]

In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank > 1 over a commutative ring (with 1/2 for the systems A 2 , F 4 , B l , C l ; with 1/2 and 1/3 for the system G 2 ) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms. This result finalizes description of automorphisms of Chevalley groups. However, the restrictions on invertible elements can be a topic of further considerations. We provide also some model-theoretic applications of this description. [ABSTRACT FROM AUTHOR]

In this paper, we show that the Δ-genus Δ (X , L) ≥ 0 for any connected polarized demi-normal scheme (X , L) over an algebraically closed field k. As an application, we obtain Δ (X , I (K X + Λ)) ≥ 0 for any KSBA stable log scheme (X , Λ) , where I is the Cartier index of K X + Λ . We also construct examples of KSBA stable log schemes with I = 1 and Δ (X , K X + Λ) = 0 , which shows the inequality is sharp when I = 1. [ABSTRACT FROM AUTHOR]

Let a be an ideal of Noetherian ring R and M a finitely generated R-module such that cd (a , M) = c . In this paper, we investigate Att R (H a c (M)) . Among other things, it is shown that Max { p ∈ Supp R M | cd (a , R / p) = c } ⊆ Att R (H a c (M)) . We also show that Att R (H a c (M)) = { p ∈ Supp R M | cd (a , R / p) = c , p = Ann R (H a c (R / p)) } and { p ∈ Supp R M | cd (a , R / p) = c , dim R / p − 1 ≤ cd (a , R / p) ≤ dim R / p } ⊆ Att R (H a c (M)). Finally, we prove that if (R , m) is a local ring and dim R / a = 1 then Att R (H a c (M)) = { p ∈ Supp R M | cd (a , R / p) = cd (a , M) } . Then by using this, it is shown that if (R , m) is a local ring then { p ∈ Supp R M | cd (a , R / p) = c , dim R / (a + p) = 1 } ⊆ Att R (H a c (M)). [ABSTRACT FROM AUTHOR]

There has been a great importance in understanding the nilpotent multipliers of finite groups in recent past. Let a group G be presented as the quotient of a free group F by a normal subgroup R. Given a positive integer c, the c-nilpotent multiplier of the group G is the abelian group M (c) (G) = (R ∩ γ c + 1 (F)) / γ c + 1 (R , F) . In particular, M (1) (G) is the Schur multiplier of G. The study of Schur multiplier of finite metacyclic groups goes back to the paper by F. R. Beyl in 1973. In this article, we study the 2-nilpotent multiplier of finite split metacyclic groups. [ABSTRACT FROM AUTHOR]

We study characterizations of sincere modules, sincere silting modules and tilting modules in terms of various vanishing conditions. Let R be a perfect ring and T be an R-module. It is proved that T is sincere silting if and only if T is presilting satisfing the vanishing condition KerExt R 0 ≤ i ≤ 1 (T , −) = 0 , and that T is tilting if and only if KerExt R 0 ⩽ i ⩽ 1 (T , −) = 0 and Gen T ⊆ KerExt R 1 ⩽ i ⩽ 2 (T , −) . As an application, we prove that a sincere silting R-module T of finite projective dimension is tilting if and only if Ext R i (T , T (J)) = 0 for all sets J and all integer i ≥ 1 . This not only extends a main result of Zhang's paper [Self-orthogonal τ-tilting modules and tilting modules, J Pure Appl Algebra, 2022, 226: 106860] from finitely generated modules over Artin algebras to infinitely generated modules over more general rings, but also gives it a different proof without using Auslander-Reiten translations. [ABSTRACT FROM AUTHOR]

The Nagata ring R(X) and the Serre’s conjecture ring R⟨X⟩ are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic polynomials, respectively. In this paper, we contribute to the study of Prüfer conditions in R(X) and R⟨X⟩. In particular, we solve the four open questions posed by Glaz and Schwarz in Section 8 of their survey paper [38] related to the transfer of Prüfer conditions to these two constructions. [ABSTRACT FROM AUTHOR]

The replacement property (or Steinitz Exchange Lemma) for vector spaces has a natural analog for finite groups and their generating sets. For the special case of the groups PSL (2 , p) , where p is a prime larger than 5, first partial results concerning the replacement property were published by Benjamin Nachman (2014). Second partial results were published by Hy P.G. Lam (2017). The main goal of this paper is to provide a complete answer for PSL (2 , p). [ABSTRACT FROM AUTHOR]

A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras k G # σ , τ k Z 2 constructed through abelian extensions of k Z 2 by k G for an abelian group G. We prove that there are only two forms of them and we get a complete list of all universal R -matrices of the generalized Kac-Paljutkin algebra H 2 n 2 (see Section 2 for the definition). [ABSTRACT FROM AUTHOR]

Let R = K [ G ] be a group ring of a group G over a field K. The Ore condition says that for any a , b ∈ R there exist u , v ∈ R such that au = bv, where u ≠ 0 or v ≠ 0. It always holds whenever G is amenable. Recently it was shown that for R. Thompson's group F the converse is also true. So the famous amenability problem for F is equivalent to the question on the Ore condition for the group ring of the same group. It is easy to see that the problem on the Ore condition for K [ F ] is equivalent to the same property for the monoid ring K [ M ] , where M is the monoid of positive elements of F. In this paper we reduce the problem to the case when a, b are homogeneous elements of the same degree in the monoid ring. We study the case of degree 1 and find solutions of the Ore equation. For the case of degree 2, we study the case of linear combinations of monomials from S = { x 0 2 , x 0 x 1 , x 0 x 2 , x 1 2 , x 1 x 2 }. This set is not doubling, that is, there are nonempty finite subsets X ⊂ M ⊂ F such that | S X | < 2 | X |. As a consequence, the Ore condition holds for linear combinations of these monomials. We give an estimate for the degree of u, v in the above equation. The case of monomials of higher degree is open as well as the case of degree 2 for monomials on x 0 , x 1 , ... , x m , where m ≥ 3. Recall that negative answer to any of these questions will immediately imply non-amenability of F. [ABSTRACT FROM AUTHOR]

We previously have developed two methods for constructing codes and designs from finite groups (mostly simple finite groups). In a recent paper we introduced a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. This new method together with background material and results required from finite groups, permutation groups and representation theory were discussed fully in that paper. The main aim of this paper is to apply the method to the first Janko sporadic simple group J 1 , for the first 3 conjugacy classes of maximal subgroups and its 2A, 3A, 5A and 7A conjugacy classes of elements. [ABSTRACT FROM AUTHOR]

Motivated by Dar and Ali's [9] elegant work's, the goal of the paper is to study nth power *-property in rings with involution and its related problems. In fact, the main result of this paper gives conditions which ensure that an additive map d : R → R satisfying nth power *-property must be X-inner. As an application, we characterize additive map F : R → R such that F (x n) = F (x) (x ∗) n − 1 + ∑ i = 1 n − 1 x i d (x) (x ∗) n − i − 1 for all x ∈ R. where d : R → R is an additive map satisfying nth power *-property. These results provide the affirmative answer to the open problem (see Problem 3.3 [9]). [ABSTRACT FROM AUTHOR]

In this paper, first we give the notion of a crossed homomorphism on a Lie triple system with respect to an action on another Lie triple system. We also construct an L ∞ -algebra using the higher derived brackets, whose Maurer-Cartan elements are crossed homomorphisms on Lie triple systems. Consequently, we obtain the twisted L ∞ -algebra that controls deformations of a given crossed homomorphism on Lie triple systems. Next we construct a cohomology theory for a crossed homomorphism on Lie triple systems and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Moreover we consider the relationship between cohomology groups of crossed homomorphisms on Lie algebras and associated Lie triple systems. [ABSTRACT FROM AUTHOR]

We study the Fano variety of k-planes Ω X (k) of a complete intersection X and show the surjectivity of the cylinder homomorphism in this setting, proving along the way the (classical) Hodge conjecture in cases where a numerical condition is satisfied. In particular, a new case is discovered in dimension 6. This work is a generalization of the second author's paper Motives of some Fano varieties. [ABSTRACT FROM AUTHOR]

The Frobenius-Perron dimension of a matrix, also known as the spectral radius, is a useful tool for studying linear algebras and plays an important role in the classification of the representation categories of algebras. In this paper, we study the Frobenius-Perron theory of the representation categories of bound quiver algebras containing loops, and find a way to calculate the Frobenius-Perron dimensions of these algebras satisfying the commutativity condition of loops. As an application, we prove that the Frobenius-Perron dimension of the representation category of a modified ADE bounded quiver algebra is equal to the maximal number of loops at each vertex. Finally, we point out that there also exist infinite dimensional algebras whose Frobenius-Perron dimensions is equal to the maximal number of loops by giving an example. [ABSTRACT FROM AUTHOR]

Let R be an associative ring with unity. A unital left R-module M is said to be distributive if for every submodules S, T and U of M, the equality S ∩ (T + U) = S ∩ T + S ∩ U holds true. In this paper, we give a necessary and sufficient condition for a direct sum of left R-modules to be distributive. This condition is given by the notion of splitting of submodules of the direct sum and the proof uses the notion of orthogonality, where both notions are discussed and revisited. [ABSTRACT FROM AUTHOR]

Consider a prime ring R which is noncommutative with the maximal left ring of quotients of R denoted by Q m l (R) and the extended centroid C. An additive map G : R → Q m l (R) satisfying G (g 2) + η g G (g) ∈ C for all g ∈ R , where η ∈ C is called a weak Jordan right η-centralizer. In this paper, we establish the characterization of weak Jordan right η-centralizers in prime rings. As an application, we describe X-generalized skew derivations which behave like weak Jordan right η-centralizers. [ABSTRACT FROM AUTHOR]

It is classical that certain truncations of the translation quiver Z Q appear in the Auslander-Reiten quiver. The stable n-translation quiver Z | n − 1 Q is introduced as a generalization of Z Q in studying higher representation theory. In this paper, we find conditions for a Hom-finite k-category to be realized as the bound path category of a convex full subquiver of a stable n-translation quiver. We show that the n-preinjective component and n-preprojective component of n-slice algebra are realized as the bound path categories of some truncations of Z | n − 1 Q o p . We also use Z | n − 1 Q o p to describe the νn-closure of Γ in the derived category. [ABSTRACT FROM AUTHOR]

In this paper we consider the Br = Br ′ question for classifying stacks by various group schemes. These are algebraic stacks that do not necessarily admit a finite flat cover by a scheme for which Br = Br ′ holds, hence are not amenable to the usual argument of pushing forward a twisted vector bundle. We provide two classes of examples satisfying Br ≠ Br ′ that do not arise from the scheme case. Communicated by Tony Varilly-Alvarado [ABSTRACT FROM AUTHOR]

Projectively coresolved Gorenstein flat modules were introduced recently by Saroch and Stovicek and were shown to be Gorenstein projective. While the relation between Gorenstein projective and Gorenstein flat modules is not well understood, the class of projectively coresolved Gorenstein flat modules is contained in the class of Gorenstein flat modules. This paper proves necessary and sufficient conditions for a module of finite Gorenstein flat dimension to be projectively coresolved Gorenstein flat, or of finite flat dimension. Stability results for the class of projectively coresolved Gorenstein flat modules are also established. [ABSTRACT FROM AUTHOR]

Green biset functors are introduced by Serge Bouc as a general framework to work with biset functors having an additional ring structure. Well-known examples include the functors of (fibered) Burnside rings, trivial source rings and character rings. Serge Bouc also introduced two generalizations of Burnside rings, the so-called slice and section Burnside rings which are also Green biset functors. In this paper, we classify simple modules over the Green biset functor of section Burnside rings. [ABSTRACT FROM AUTHOR]