Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 1
Abstract
In this short paper we study for the skew P BW (Poincar-Birkhoff-Witt) extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew P BW extensions include a considerable number of non-commutative rings of polynomial type such that classical P BW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.
Authors and Affiliations
Oswaldo Lezama
Keywords
Related Articles
- EP ID EP394546
- DOI 10.7151/dmgaa.1264
- Views 50
- Downloads 0
NONDISTRIBUTIVE RINGS AND THEIR ORE ¨ LOCALIZATIONS
In the paper, we introduce the notion of a nondistributive ring N as a generalization of the notion of an associative ring with unit, in which the addition needs not be abelian and the distributive law is replaced by n0...
Relative determinant of a bilinear module
The aim of the paper is to generalize the (ultra-classical) notion of the determinant of a bilinear form to the class of bilinear forms on projective modules without assuming that the determinant bundle of the module is...
ALL REGULAR-SOLID VARIETIES OF IDEMPOTENT SEMIRINGS
The lattice of all regular-solid varieties of semirings splits in two complete sublattices: the sublattice of all idempotent regular-solid varieties of semirings and the sublattice of all normal regular-solid varieties o...
A NOTE ON IDEAL BASED ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING
In this paper, we consider the ideal based zero divisor graph ΓI (R) of a commutative ring R. We discuss some graph theoretical properties of ΓI (R) in relation with zero divisor graph. We also relate certain parameters...
Bi-Interior Ideals of Semigroups
In this paper, as a further generalization of ideals, we introduce the notion of bi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of semigroup and study the properties of bi-interior idea...