Right Buchberger algorithm over bijective skew PBW extensions

TL;DR

This paper develops a right Buchberger algorithm for bijective skew PBW extensions, enabling computation of right Gr"obner bases, which is essential for advancing algebraic tools and applications in this area.

Contribution

It introduces a right version of the Buchberger algorithm and related reduction theory for bijective skew PBW extensions, complementing existing left algorithms.

Findings

Implemented the right Buchberger algorithm in Maple using SPBWE.lib.

Demonstrated examples of the algorithm's application.

Facilitated the development of homological algebra tools for skew PBW extensions.

Abstract

In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right division algorithm and generate a right version of Buchberger algorithm over bijective skew PBW extensions, finally we illustrate some examples using the SPBWE.lib library implemented in Maple (see [1], [4]). It is important to note that the development of this theory is fundamental to complete the SPBWE.lib library and to be able to develop many of the homological applications that arise as result of obtaining the right Gr\"obner bases over skew PBW extensions.