Let S be a polynomial ring in n variables over a field K of characteristic 0. A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free S-module is given. 2010 Mathematics Subject Classification: 13B25, 13D02, 16W50.

The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

Let R be an irreducible root system with the Coxeter number h. Let l > h be an odd integer (we assume that l is not divisible by 3 if R is of type G2). Let U be the quantum group of type 1 with divided powers associated to these data, see [10] (of type 1 means that the elements K l i are equal to 1). Let u ⊂ U be the Frobenius kernel, see loc. cit. Let 1 be the trivial U−module. The cohomology ...

We study the irregularity sheaves attached to the A-hypergeometric D-module MA(β) introduced by Gel’fand et al., where A ∈ Z d×n is pointed of full rank and β ∈ C. More precisely, we investigate the slopes of this module along coordinate subspaces. In the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector L on torus...

We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebra structures on the Witt algebra are classified. All of them are simple and they in...

A notion of curvature is introduced in multivariable operator theory. The curvature invariant of a Hilbert module over C[z(1),., z(d)] is a nonnegative real number which has significant extremal properties, which tends to be an integer, and which is hard to compute directly. It is shown that for graded Hilbert modules, the curvature agrees with the Euler characteristic of a certain finitely gen...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of classical strongly 2-absorbing second submodules modules over rings. A number results concerning these classes their homogeneous components are given.

Let $G$ be a group, $R$ $G$-graded commutative ring with identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, new concept $S$-primary submodules is introduced as generalization Primary well $S$-prime $M$. Also, some properties class are investigated.

Hyperoctahedral homology for involutive algebras is the theory associated to hyperoctahedral crossed simplicial group. It related equivariant stable homotopy via of infinite loop spaces. In this paper we show that there an E-infinity algebra structure on module computes homology. We deduce admits Dyer-Lashof operations. Furthermore, a Pontryagin product which gives associative, graded-commutati...

Let k be a field and S = k[x1, . . . , xn] be a polynomial ring over k. We consider finite sequences of homogeneous polynomials of positive degrees and their operation on non-trivial finitely generated graded S-modules (with grading in Z). Here and in the following, by a polynomial, we always mean an element of S. Moreover, by an S-module we mean in the following a graded S-module with grading ...