Two-Sided Noncommutative Gr\"{o}bner Basis on Quiver Algebras
Abstract
For a quiver , we define a path algebra as a span of all the paths of positive length. We study left (respective right) sided ideals and their Gr\"{o}bner bases. We introduce the two-sided ideals, two-sided division algorithm for elements of and study the two-sided Gr\"{o}bner bases. We show that with the defined two-sided division algorithm and two-sided Buchberger's algorithm, we can find a finite or an infinite Gr\"{o}bner basis for a two-sided ideal given a fixed admissible ordering.
Keywords
Cite
@article{arxiv.2306.06457,
title = {Two-Sided Noncommutative Gr\"{o}bner Basis on Quiver Algebras},
author = {Daniel K. Waweru and Damian M Maingi},
journal= {arXiv preprint arXiv:2306.06457},
year = {2023}
}
Comments
Presented at the International Conference on Stochastic Processes and Algebraic Structures, Sweden, 2019. To appear as a chapter in the book "Non-Commutative and Non-Associative Algebra and Analysis Structures", Springer Proceedings in Mathematics & Statistics, 2023