Right Buchberger Algorithm over Bijective Skew PBW Extensions

Article type: Research Article

Authors: Fajardo, William^{; *}

Affiliations: Seminario de Álgebra Constructiva - SAC², Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia. wafajardoc@unal.edu.co

Correspondence: [*] Address for correspondence: Seminario de Álgebra Constructiva - SAC2, Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia.

Abstract: In this paper we present a right version of the Buchberger algorithm over skew Poincaré-Birkhoff-Witt extensions (skew PBW extensions for short) defined by Gallego and Lezama [5]. This algorithm is an adaptation of the left case given in [3]. In particular, we developed a right version of the division algorithm and from this we built the right Grbner bases theory over bijective skew PBW extensions. The algorithms were implemented in the SPBWE library developed in Maple, this paper includes an application of these to the membership problem. The theory developed here is fundamental to complete the SPBWE library and thus be able to implement various homological applications that arise as result of obtaining the right Grbner bases over skew PBW extensions.

Keywords: Non-commutative computational algebra, skew PBW extensions, Buchberger algorithm, Grbner bases, SPBWE library, Maple

Keywords: Mathematics Subject Classification. 2021: Primary: 16Z05. Secondary: 16D40, 15A21

DOI: 10.3233/FI-2021-2093

Journal: Fundamenta Informaticae, vol. 184, no. 2, pp. 83-105, 2021