Filtered-graded transfer of noncommutative Gr\"obner bases

TL;DR

This paper demonstrates a method to transfer Gr"obner bases between a bijective skew PBW extension and its associated graded ring, extending computational techniques in noncommutative algebra.

Contribution

It introduces a filtered-graded transfer technique for Gr"obner bases in bijective skew PBW extensions, expanding computational tools in noncommutative algebra.

Findings

Transfer of Gr"obner bases is possible between skew PBW extensions and their graded rings.

The method applies to free $K$-algebras and PBW algebras.

Enhances computational approaches in noncommutative algebra.

Abstract

As the case of free $\Bbbk$-algebras and $PBW$ algebras, given a bijective skew $PBW$ extension $A$, we will show that it is possible transfer Gr\"obner bases between $A$ and its associated graded ring.