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arXiv · 2306.06457

Two-Sided Noncommutative Gr\"{o}bner Basis on Quiver Algebras

Daniel K. Waweru·Damian M Maingi
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Abstract

For a quiver $Q$, we define a path algebra $KQ$ 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 $KQ$ 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 $I \subseteq KQ$ given a fixed admissible ordering.

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Daniel K. Waweru, Damian M Maingi. 2023-06-10. Two-Sided Noncommutative Gr\"{o}bner Basis on Quiver Algebras. https://doi.org/10.1007/978-3-031-32009-5_30

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