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We investigate the notions of weak annihilator and nilpotent associated prime defined by Ouyang and Birkenmeier (Weak annihilator over extension rings, 2012) in the setting of skew PBW extensions. We extend several results formulated in the literature concerning annihilators and associated primes of commutative rings and skew polynomial rings to a more general setting of algebras not considered before. We exemplify our results with families of algebras appearing in the theory of enveloping algebras, noncommutative algebraic geometry, and theoretical physics. Finally, we present some ideas for future research. [ABSTRACT FROM AUTHOR]

The study of invariants of group actions on commutative polynomial rings has motivated many developments in commutative algebra and algebraic geometry. It has been of particular interest to understand what conditions on the group result in an invariant ring satisfying useful properties. In particular, Watanabe's Theorem states that the invariant subring of k [ x 1 , ... , x n ] under the natural action of a finite subgroup of S L n (k) is always Gorenstein. In this paper, we study this question in the more general setting of group actions on noncommutative non-connected algebras A. We develop the notion of a homological determinant of an automorphism of A, then use the homological determinant to study actions of finite groups G on A. We give a sufficient condition so that the invariant ring AG has finite injective dimension and satisfies the generalized Gorenstein condition. More precisely, let A be a noetherian N -graded generalized Gorenstein algebra with finite global dimension. Suppose all elements of G fix the idempotents of A and act with trivial homological determinant. Then the invariant ring AG is generalized Gorenstein. [ABSTRACT FROM AUTHOR]

In this article, we define the notion of Brauer-Clifford group for H-locally finite (S, H)-Azumaya algebras, when H is a cocommutative Hopf algebra and S is an H-locally finite commutative H-module algebra over a commutative noetherian ring k. This is the situation that arises in applications with connections to algebraic geometry. This Brauer-Clifford group turns out to be an example of a Brauer group of a symmetric monoidal category. [ABSTRACT FROM AUTHOR]

A depiction of a nonnoetherian integral domain R is a special coordinate ring that provides a framework for describing the geometry of R. We show that if R is noetherian in codimension 1, then R has a unique maximal depiction T. In this case, the geometric dimensions of the points of Spec R may be computed directly from T. If in addition R has a normal depiction S, then S is the unique maximal depiction of R. [ABSTRACT FROM AUTHOR]

Let ⟨ K, ν ⟩ be a real closed valued field, and letS ⊆ Knbe an open semialgebraic set. Using tools from model theory, we find an algebraic characterization of rational functions which admit, onS, only values in the valuation ring. We use this result to deduce a criterion for a rational function to be bounded on an open semialgebraic subset of some irreducible variety over a real closed field or over an ordered field which is dense in its real closure. [ABSTRACT FROM AUTHOR]

We construct a class of projective rational varieties X of any dimension m ≥ 1, which are smooth except at a point O, with the projective space ℙ m as normalization, having smooth branches, and reduced projectivized tangent cone in O. The Hilbert function of X is considered and is explicitly computed when the point O is seminormal. Indeed, we study seminormality, obtaining necessary and sufficient conditions for O to be seminormal and show that in such case the tangent cone is reduced and seminormal. [ABSTRACT FROM PUBLISHER]

We present a decomposition of the space of twisted arcs of a toric stack. As a consequence, we give a combinatorial description of the motivic integral associated to a torus-invariant divisor of a toric stack. [ABSTRACT FROM AUTHOR]

Using the categorical equivalence of the class of generalized MV-algebras with the class of unital ℓ-groups, we describe all varieties of symmetric top abelian unital ℓ-groups that cover the variety Auℓ of abelian unital ℓ-groups. Equivalently, we describe all cover varieties of the variety of MV-algebras, MV, within the variety of generalized MV-algebras admitting only one negation and each of whose maximal ideals is normal. In particular, there are continuum many representable varieties of generalized MV-algebras that cover MV. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e., a graded A-linear homomorphism ∇: Derk(A) → Endk(M), that satisfies the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring [image omitted] admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module. [ABSTRACT FROM AUTHOR]

We prove that a finite-dimensional algebra over an algebraically closed field is of derived dimension 0 if and only if it is an iterated tilted algebra of Dynkin type. [ABSTRACT FROM AUTHOR]

For a prime p, we denote by Bn the cyclic group of order pn. Let φ be a faithful irreducible character of Bn, where p is an odd prime. We study the p-group G containing Bn such that the induced character φG is also irreducible. The purpose of this article is to determine the subgroup NG(NG(Bn)) of G under the hypothesis [NG(Bn):Bn]4 ≦ pn. [ABSTRACT FROM AUTHOR]

We give a presentation for the Chow ring of the moduli space of degree 2 stable maps from 2-pointed rational curves to the projective line. Also, integrals of all degree 4 monomials in the hyperplane pullbacks and boundary divisors of this ring are computed using equivariant intersection theory. Finally, the presentation is used to give a new computation of the (previously known) values of the genus zero, degree 2, 2-pointed gravitational correlators of the projective line. [ABSTRACT FROM AUTHOR]

As an outgrowth of the study of algebraic geometry over groups, discriminating groups were introduced. Many important universal type groups such as Higman's universal group and Thompson's group F were shown to be discriminating. Squarelike groups were then introduced to better capture axiomatic properties of discrimination. In the present article squarelike groups are reinterpreted in terms of discrimination of quasi varieties, and the relationship with an older version of discrimination, termed varietal discrimination here, is studied. [ABSTRACT FROM AUTHOR]

We consider a Birman, Ko, and Lee (BKL) presentation (defined by Vershinin, 2003) for the semigroup of singular braids SB n . We prove the embedding property for the monoid of positive singular braids and give a solution to the word and conjugacy problems in BKL generators. [ABSTRACT FROM AUTHOR]

We explicitly compute the equations and components of the jet schemes of a monomial subscheme of affine space from an algebraic perspective. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to construct the character tables of the parabolic subgroups of the Chevalley groups G 2 ( q ), where q is a power of a prime p > 3. [ABSTRACT FROM AUTHOR]

The purpose of this article is to try to determine the error term in Vojta's height inequality for algebraic points over function fields. [ABSTRACT FROM AUTHOR]

Type III unprojection plays a very important role in the birational geometry of Fano threefolds (cf. Corti et al., 2000; Reid, 2000). According to Reid (2000, p. 43), it was first introduced by A. Corti on his calculations of Fano threefolds of genus 6 and 7. It seems that at present a general definition of Type III unprojection is still missing. After proving some general facts about residual ideals in Section 2, we propose a definition for the generic Type III unprojection (Definition 3.3), and prove in Theorem 3.5 that it gives a Gorenstein ring. Communicated by W. Bruns [ABSTRACT FROM AUTHOR]

This article provides new, relatively simple proofs of some important results about unipotent classes in simple linear algebraic groups. We derive the formula for the Jordan blocks of the Richardson class of a parabolic subgroup of a classical group. This result was originally due to Spaltenstein. Secondly, we derive the description of the natural partial order of unipotent classes in the general linear group in terms of their Jordan blocks. This result was originally due to Gerstenhaber. Finally, we obtain a proof of the Bala-Carter Theorem, which holds even in certain bad characteristics. This proof requires the prior knowledge of the number of unipotent classes, unlike the original proofs due to Bala, Carter and Pommerening. [ABSTRACT FROM AUTHOR]

In this article, using the local parametric equations of a generic projection π of a smooth projective variety X , at an analytically irreducible singular point y of X ′ = π( X ), the defining ideals J and J ′ of X ′ and its singular locus at y are expressed as ideals of maximal and sub-maximal minors of certain Sylvester matrix 𝒬. The proof is obtained by a convenient reduction of 𝒬 to a “generic pluri-circulant matrix” P and the construction of minimal Gröbner bases for the ideal of t -minors of P and for the ideals J and J ′. The depth of local rings of X ′ and Sing( X ′) at y are also computed in terms of the multiplicity at y . [ABSTRACT FROM AUTHOR]

For projective codimension two surfaces and threefolds whose singular locus is one dimensional, we get the sharp Castelnuovo-Mumford regularity bound in terms of degrees of defining equations and give the classification of nearly extremal cases. This is a generalization of the result of Bertram et al. [ABSTRACT FROM AUTHOR]

Using the local subgroup strategy of An and O'Brien (1997), An and O'Brien (1999), we classify the radical subgroups and chains of the Fischer simple group Fi 22 and verify the Alperin weight conjecture and the Uno reductive conjecture for this group; the latter is a refinement of the Dade reductive and Isaacs–Navarro conjectures. [ABSTRACT FROM AUTHOR]

On vérifie, en degré d ≤ 11, la conjecture suivante:“le schéma de Hilbert des courbes lisses connexes de degré d et de genre g de l'espace projectifá trois dimensions sur le corps des complexes est irréductible pour g ≤ 2d − 9” ABSTRACT We check that the following conjecture holds true for d ≤ 11 :“the Hilbert scheme of smooth and connected space curves of degree d and genus g is irreducible provided that g ≤ 2d − 9.” [ABSTRACT FROM AUTHOR]

Let G ⊂ SO(4) denote a finite subgroup containing the Heisenberg group. In this paper we classify all such groups, we find the dimension of the spaces of G-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding G-invariant pencils of surfaces in [Popf]3 which we started in Sarti [Sarti, A. (2000). Pencils of symmetric surfaces in [Popf]3(C). J. Algebra 246:429–452]. It turns out that we have five more pencils, two of them containing surfaces with nodes. [ABSTRACT FROM AUTHOR]

Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph Δ(G) of G is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ϵ cd(G). In this paper, we determine the graph Δ(G) when G is a finite simple group of exceptional Lie type. [ABSTRACT FROM AUTHOR]

In this article we prove Broué's conjecture on isotypies for the case of principal blocs of Sp(4, Fq)〈σ〉 : a split cyclic extension of the symplectic group of dimension 4 over a finite field Fq for q odd. The core of the proof is to lift to the group Sp(4, Fq)〈σ〉 an isotypy of the group Sp(4, Fq). For this purpose, we build a convenient version of a theorem of lifting isotypies. [ABSTRACT FROM AUTHOR]

We prove that there exists an integer M such that if S ⊂ [Popf]4 is a smooth surface with deg(S) > M, then the canonical map of S is birational. Then we consider surfaces, S, satisfying hi([Iscr]S(3 − i)) = 0, 0 ≤ i ≤ 2 and show that they are regular and that their canonical system is base point free and very ample if deg(S) > M and S doesn't contain −2-curves. [ABSTRACT FROM AUTHOR]

The concept of a composed product for univariate polynomials has been explored oextensively by Brawley, Brown, Carlitz, Gao, Mills et al. Starting with these fundamental ideas and using fractional power series representation of bivariate polynomials, the current authors Mills and Neuerburg [Mills, D., Neuerburg, K. M. A bivariate analogue to the composed product of polynomials. Algebra Colloquium (to appear)] generalize the univariate results by defining and investigating a bivariate composed sum, composed multiplication, and composed product (based on function composition) for certain classes of bivariate polynomials. In this, the sequel, we extend the generalizations to certain classes of multivariate polynomials, written as f(x1,…,xn), over an algebraically closed field of characteristic zero. In particular, we consider a composed sum and composed multiplication defined on the class of quasiordinary polynomials. We then consider what algebraic structure is imposed by these operations. Next, we consider a generalization of the geometry associated with the class of ν-quasiordinary polynomials. Finally, we utilize this geometry to show that an algorithm given by Gao and Lauder [Gao, S., Lauder, A. G. B. (2001). Decomposition of polytopes and polynomials. Discrete Comput. Geom. 26(1):89–104] to determine whether a given bivariate polynomial is absolutely irreducible over a given field can be used to ascertain whether a given trivariate polynomial that factors completely in one variable decomposes according to the composed multiplication operation. [ABSTRACT FROM AUTHOR]

Recently Jain, López-Permouth and Syed classified indecomposable non-local right continuous right π-rings. In the present article we describe the structure of right continuous right π-rings. [ABSTRACT FROM AUTHOR]

In this note we prove that a smooth order satisfying the reverse geometric engineering conditions in stringtheory of Berenstein (Berenstein, D. Reverse geometric engineering of singularities, arXiv:hep-th/0201093, Sec. 2) (in any compactifying dimension) is Auslander regular. Moreover, we classify the étale local structure of smooth orders over an isolated central singularity. [ABSTRACT FROM AUTHOR]

Based on tilting theory, we demonstrate the existence of homogeneous deformations for the Brauer tree algebras, which are derived naturally from a tilting complex. [ABSTRACT FROM AUTHOR]

Lie quasi-bialgebras (also called Jacobian quasi-bialgebras) are generalisations of Lie bialgebras while di3erential quasi-Batalin-Vilkovisky algebras are generalisations of di3erential Batalin-Vilkovisky algebras. We show that the kernel of the Laplacian operator of a quasi-Batalin-Vilkovisky algebra is a homotopy BV-algebra (BV[SUB∞]-algebra). We establish a one-to-one correspondence between the Lie quasi-bialgebra structures on a finite-dimensional vector space with a generalized co-character and differential quasi-Batalin-Vilkovisky structures on the exterior algebra of the dual vector space. [ABSTRACT FROM AUTHOR]

Some observations and conjectures concerning finite dimensional associative commutative algebras that are degenerations of semisimple algebras. “…on sait qu'on ne sait rien sur cette sorte d'algèbre.” André Weil [ABSTRACT FROM AUTHOR]

We will give a new short proof of Bezout's Theorem for complex algebraic curves in P2 which is local. [ABSTRACT FROM AUTHOR]