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This article is intended to indicate and discuss some errors in N. Lavi’s paper “A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions”. [ABSTRACT FROM AUTHOR]

A theorem in the article “Characterization of Monoids by Properties of Generators,” written by Kilp and Knauer, states that amalgamated coproducts of generators are generators in the categoryAct-S of right S-acts over a monoid S. In this note we give a counterexample to deny this theorem. However, we show that the results in that article based on the mentioned theorem still remain valid. Moreover, an incorrect proposition in the monographMonoids, Acts and Categoriesby Kilp et al. which states that coamalgamated product of cogenerators are cogenerators is denied by a counterexample. [ABSTRACT FROM PUBLISHER]

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]

A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [3], Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. The aim of the present paper is to prove that an analogous dichotomy holds for commutative rings with 1 as well. [ABSTRACT FROM AUTHOR]

Let A be a brace algebra. This structure implies that A is also a pre-Lie algebra. In this paper, we establish Composition-Diamond lemma for brace algebras. For each pre-Lie algebra L, we find a Gröbner-Shirshov basis for its universal brace algebra Ub(L). As applications, we determine an explicit linear basis for Ub(L) and prove that L is a pre-Lie subalgebra of Ub(L). [ABSTRACT FROM AUTHOR]

Let (R, 𝔪) be a complete local ring, 𝔞 an ideal ofR, andMa finitely generatedR-module. The aim of this paper is to show that for any non-negative integern,, whereis thenth finiteness dimension ofMrelative to 𝔞. As a consequence, it follows that the setis finite. This generalizes the main result of Quy [10] and Brodmann and Lashgari [4]. [ABSTRACT FROM AUTHOR]

LetGbe a finite group andkan algebraically closed field of characteristicp. In this paper we investigate the Loewy structure of centers of indecomposable group algebraskG, for groupsGwith a normal elementary abelian Sylowp-subgroup. Furthermore, we show a reduction result for the case that a normal abelian Sylowp-subgroup is acted upon by a subgroup of its automorphism group; this is fundamental in providing generic formulae for the Loewy lengths considered. [ABSTRACT FROM AUTHOR]

In this paper, we study the graded Thierrin radical and the classical Thierrin radical of a graded ring, which is the direct sum of a family of its additive subgroups indexed by a nonempty set, under the assumption that the product of homogeneous elements is again homogeneous. There are two versions of this graded radical, the graded Thierrin and the large graded Thierrin radical. We establish several characterizations of the graded Thierrin radical and prove that the largest homogeneous ideal contained in the classical Thierrin radical of a graded ring coincides with the large graded Thierrin radical of that ring. [ABSTRACT FROM AUTHOR]

For a finite groupG, let |Cent(G)| andω(G) denote the number of centralizers of its elements and the maximum size of a set of pairwise noncommuting elements of it, respectively. A groupGis calledn-centralizer if |Cent(G)| = nand primitiven-centralizer if. In this paper, among other results, we find |Cent(G)| andω(G) whenis minimal nonabelian and this generalizes some previous results. We give a necessary and sufficient condition for a primitiven-centralizer groupGwith the minimal nonabelian central factor. Also we show that if, thenGis a primitive 14-centralizer group andω(G) = 10 or 13. Finally we confirm Conjecture 2.4 in [A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq. 7(2) (2000), 139-146]. [ABSTRACT FROM AUTHOR]

In a recent paper by the authors, the associative and the Lie algebras of Weyl type A[D] = A ⊗ F[D] were introduced, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0 and D consisting of locally finite derivations of A, is studied. The isomorphism classes of these associative and Lie algebras are determined. The structure of these algebras is described explicitly. [ABSTRACT FROM AUTHOR]

Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series ringsR((x−1;σ,δ)), whereRis an associative ring equipped with an automorphismσand aσ-derivationδ. [ABSTRACT FROM PUBLISHER]

This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classification is reduced to classifying the solvableChermak–Delgado simple groups, which the author defines. The notion of “Chermak–Delgado simple,” or “CD-simple” for short, is a generalization of simple groups through the Chermak–Delgado lattice. The author completes a classification of Chermak–Delgado simple groups under certain restrictions on the primes involved in the group order. [ABSTRACT FROM PUBLISHER]

In this paper we provide conditions under which automorphism-coinvariant modules over a right perfect ring are quasi-projective. [ABSTRACT FROM PUBLISHER]

All groups considered in this paper are finite. A subgroupHof a groupGis said to beSS-permutableorSS-quasinormalinGifHhas a supplementKinGsuch thatHpermutes with every Sylow subgroup ofK. Following [6], we call a groupGanSST-groupprovided that SS-permutability is a transitive relation inG, that is, ifAis an SS-permutable subgroup ofBandBis an SS-permutable subgroup ofG, thenAis an SS-permutable subgroup ofG. The main aim of this paper is to present several characterisations of soluble SST-groups. [ABSTRACT FROM PUBLISHER]

This paper deals with the variety of commutative algebras satisfying the identity β{(yx2)x − ((yx)x)x} + γ{yx3 − ((yx)x)x} = 0, where β, γ are scalars. These algebras appeared as one of the four families of degree four identities in Carini, Hentzel, and Piacentini-Cattaneo [6]. We give a characterization of representations and irreducible modules on these algebras. Our results require that the characteristic of the ground field is different from 2, 3. [ABSTRACT FROM PUBLISHER]

In this paper, all finite groups whose commuting (noncommuting) graphs can be embed on the plane, torus, or projective plane are classified. [ABSTRACT FROM PUBLISHER]

In this paper we consider the Hilbert schemeparameterizing subschemes of ℙnwith Hilbert polynomialp(t), and we investigate its locus containing points corresponding to schemes with regularity lower than or equal to a fixed integerr′. This locus is an open subscheme ofand, for everys ≥ r′, we describe it as a locally closed subscheme of the Grasmanniangiven by a set of equations of degree ≤deg(p(t)) +2 and linear inequalities in the coordinates of the Plücker embedding. [ABSTRACT FROM PUBLISHER]

In this paper we extend the study of total graphs τ(R) to noncommutative finite ringsR. We prove that τ(R) is connected if and only ifRis not local, and we see that in that case τ(R) is always Hamiltonian. We also find an upper bound for the domination number of τ(R) for all finite ringsR. [ABSTRACT FROM PUBLISHER]

In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined. [ABSTRACT FROM PUBLISHER]

The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the Weyl arrangement and their parallel translations. It was introduced by J.-Y. Shi in the study of the Kazhdan–Lusztig representation of the affine Weyl groups. M. Yoshinaga showed that the cone over every Shi arrangement is free. In this paper, we construct an explicit basis for the derivation module of the cone over the Shi arrangements of the typeBℓorCℓ. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x,y) → x○yand (x,y) → x/yfromH × Hto 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset ofHis a complete part, then the fundamental group ofHis a topological group. It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett. [ABSTRACT FROM AUTHOR]

Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimensionn ≥ 6 and nilindexn − 1 based on the condition thatn − 4 ≤ dim 𝔄3 ≤ n − 3. This paper is a continuation of [10], where we describe commutative power-associative nilalgebras of dimension and nilindexn. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2]. [ABSTRACT FROM AUTHOR]

In 1967, Shioda [20] determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in [20] are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed fieldk, chark ≠ 2, 3, 5, 7. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants. [ABSTRACT FROM PUBLISHER]

In this paper, we give the characterization of unmixedf-ideals of degreed ≥ 2 generalizing the results given in [1]. [ABSTRACT FROM PUBLISHER]

In this paper, we give a new simple algebraic proof of the involutivity of the characteristic variety after Gabber, which is one of the most important results ofD-module theory. [ABSTRACT FROM AUTHOR]

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in [3]. In this paper, closed formulae of the finite split oscillator dictionary 𝔖sare revisited by a simple proof, the structure of nonsplit tori of the groupSL(2, 𝔽p) is studied, and an explicit algorithm for computing the finite nonsplit oscillator dictionary 𝔖nsis described. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module. [ABSTRACT FROM AUTHOR]

In this paper, we give an algorithm to find the roots of the octonionic quadratic equationx2 + bx + c = 0, and develop a Matlab package to find solutions. We also discuss how to find the roots of some other octonion quadratic equations, such as an algorithm is given for finding the roots of the octonion quadratic equationxax + bx + c = 0. [ABSTRACT FROM AUTHOR]

For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type ℒ2 introduced by Camacho, Gómez, González and Omirov, all possible right and left solvable indecomposable extensions over the field ℝ are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper. [ABSTRACT FROM AUTHOR]

A submodule N of a module M is δ-small in M if N+X≠M for any proper submodule X of M with M∕X singular. A projective δ-cover of a module M is a projective module P with an epimorphism to M whose kernel is δ-small in P. A module M is called δ-semiperfect if every factor module of M has a projective δ-cover. In this paper, we prove various properties, including a structure theorem and several characterizations, for δ-semiperfect modules. Our proofs can be adapted to generalize several results of Mares [8] and Nicholson [11] from projective semiperfect modules to arbitrary semiperfect modules. [ABSTRACT FROM AUTHOR]

In this paper, we introduce von Neumann regular modules and give many characterizations of von Neumann regular modules. Further, we investigate the relations between von Neumann regular modules and other classical modules. Finally, we characterize Noetherian von Neumann regular modules. [ABSTRACT FROM AUTHOR]

The main result of this paper gives a classification of commutative association schemes, all irreducible characters of which have multiplicity 1 or a prime p. [ABSTRACT FROM AUTHOR]

Leibniz algebras are certain generalization of Lie algebras. Recently, analyzing the structure of subalgebras, David Towers gave some criteria for the solvability and supersolvability of Lie algebras. In this paper we define analogues concepts for Leibniz algebras and extend some of these results on solvability and supersolvability to that of Leibniz algebras. [ABSTRACT FROM AUTHOR]

In this paper, the regular endomorphisms of the join of split graphs are investigated. We give a condition under which the regular endomorphisms of the join of split graphs form a monoid. [ABSTRACT FROM AUTHOR]

Given a family of commutative rings { R a } a? A , we investigate the family ??(? a? A R a ) of Artinian subrings of ? a? A R a . This paper deals also with the question of when a pair (? a? A R a , ? a? A T a ) is zero-dimensional, where {( R a , T a )} a? A is a family of zero-dimensional pairs. [ABSTRACT FROM AUTHOR]

Orthodox semigroups have been studied by many authors, in particular by Hall, Yamada and Petrich. In this paper, we give the standard representation of orthodox semigroups and investigate various e-varieties of orthodox semigroups which are determined by the standard representations. [ABSTRACT FROM AUTHOR]

In this paper we discuss, in terms of quiver with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension at most two and we give a sufficient condition to be a quasitilted algebra. We show that this condition is not necessary. In the case of a strongly simply connected schurian algebra, we discuss necessary conditions, and combining both types of conditions, we are able to analyze if some given algebra is quasitilted. As an application we obtain the quiver with relations of all the tilted and cluster tilted algebras of Dynkin typeEp. [ABSTRACT FROM AUTHOR]

A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e., groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgroup is non-trivial, the group is called a generalizedT2-group. In particular, we provide structure results for such groups, investigate their nilpotency class, and construct examples of finitep-groups which are generalizedT2-groups. [ABSTRACT FROM AUTHOR]

Higher rank Brill–Noether theory is completely known for curves of genus ≤ 3. In this paper, we investigate the theory for curves of genus 4. Some of our results apply to curves of arbitrary genus. [ABSTRACT FROM AUTHOR]

For a finite groupG, letn(G) denote the number of conjugacy classes of non-subnormal subgroups ofG. In this paper, we show that a finite groupGsatisfyingn(G)≤2|π(G)| is solvable, and for a finite non-solvable groupG,n(G) = 2|π(G)|+1 if and only ifG≅A5. [ABSTRACT FROM AUTHOR]

In this paper, we prove that every standard Koszul (not necessarily graded) standardly stratified algebra is also Koszul. This generalizes a similar result of [3] on quasi-hereditary algebras. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan–Hölder theorem for chief series. [ABSTRACT FROM PUBLISHER]

Let, whereSnis the symmetric group onXnandPKn,ris the semigroup of partial mapssuch that |im(α)| ≤ rfor 1 ≤ r ≤ n − 1. In this paper, we find necessary and sufficient conditions for any subset ofPKn,rto be a (minimal) relative generating set of the subsemigroupPTn,rmoduloSn. Then, for each 1 ≤ r ≤ n − 1, we show that the smallest number of elements ofPKn,rwhich, together withSn, generatePTn,riswherepr(n − s) is the number of partitions ofn − swithrterms. We also consider, whereAnis the alternating group onXn. [ABSTRACT FROM AUTHOR]

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples. [ABSTRACT FROM PUBLISHER]

LetGbe a finite group, andT(G) be the sum of all complex irreducible character degrees ofG. In this paper, we get the exact lower bound of |G|∕T(G) for a non-r-solvable groupG. [ABSTRACT FROM AUTHOR]

The variety of restriction semigroups may be most simply described as that generated from inverse semigroups (S, ·,−1) by forgetting the inverse operation and retaining the two operationsx+ = xx−1andx* = x−1x. The subvarietyBofstrictrestriction semigroups is that generated by the Brandt semigroups. At the top of its lattice of subvarieties are the two intervals [B2,B2M = B] and [B0,B0M]. Here,B2andB0are, respectively, generated by the five-element Brandt semigroup and that obtained by removing one of its nonidempotents. The other two varieties are their joins with the variety of all monoids. It is shown here that the interval [B2,B] is isomorphic to the lattice of varieties of categories, as introduced by Tilson in a seminal paper on this topic. Important concepts, such as the local and global varieties associated with monoids, are readily identified under this isomorphism. Two of Tilson's major theorems have natural interpretations and application to the interval [B2,B] and, with modification, to the interval [B0,B0M] that lies below it. Further exploration may lead to applications in the reverse direction. [ABSTRACT FROM PUBLISHER]

In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories areℤ3andS3. We also show that the only nonsolvable group with two supercharacter theories isSp(6,2). [ABSTRACT FROM PUBLISHER]

In this paper, we provide a description of the torsion parts for the components in the partial Schur multiplierpM(G) of a groupG. This allows us to classify the finite groups and finitely generated abelian groups having partial Schur multiplier consisting only of trivial components. Also the study of the torsion parts ofpM(G) permits us to characterize finite groups for which the total components ofpM(G) are isomorphic to the multiplicative group of the base field. [ABSTRACT FROM PUBLISHER]

A groupGis said to be aB(n,k) group if for anyn-element subsetAofG, |A2| ≤k. In this paper, a characterization ofB(5, 18) groups is given. It is shown thatGis aB(5, 18) group if and only if one of the following statements holds: (1)Gis abelian; (2) |G| ≤18; (3)G ≅ ⟨ a,b | a5 = b4 = 1,ab = a−1 ⟩. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to define representations and a cohomology of Horn-Lie color algebras and to study some key constructions and properties. We describe Hartwig-Larsson-Silvestrov Theorem in the case of V-graded algebras, study one-parameter formal deformations, discuss αk-generalized derivations and provide examples. [ABSTRACT FROM AUTHOR]