Projective modules and Gröbner bases for skew PBW extensions

1786 - 0091 Gröbner Bases of Modules over Σ − Pbw Extensions

For σ−PWB extensions, we extend to modules the theory of Gröbner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative σ − PWB extension, we compute the module of syzygies of a submodule of the free module A.

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...

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.

Gröbner bases and syzygies on bimodules over PBW algebras

A new method for the computation of two-sided Gröbner bases of ideals and bimodules shifting the problem to the enveloping algebra is proposed. This alternative method appears to be more efficient than the one in [Kandri-Rody, A., Weispfenning, V., 1990. Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Comput. 9, 1–26] since it calls the left Buchberger algorithm once. We...

Interactions between non-commutative algebraic geometry and skew PBW extensions