Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

Interactions between non-commutative algebraic geometry and skew PBW extensions

BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

Non-commutative Algebraic Geometry

0 Introduction This is a reasonably faithful account of the ve lectures I delivered at the summer course \Geometria Algebraica no Commutativa y Espacios Cuanti-cos" for graduate students, in Spain, July 25{29, 1994. The material covered was, for the most part, an abridged version of Artin and Zhang's paper 2]. Fix a eld k. Given a Z-graded k-algebra, A say, which for simplicity is assumed to be...

Jacobson’s conjecture and skew PBW extensions

The aim of this paper is to compute the Jacobson’s radical of skew PBW extensions over domains. As a consequence of this result we obtain a direct relation between these extensions and the Jacobson’s conjecture, which implies that skew PBW extensions over domains satisfy this conjecture.

Homological Computations in PBW Modules

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Exti (M,N) is provided when N is a centralizing bimodule. Mathematics Subject Classifications (2000): 16Z05, 16E30.