Two-Sided Noncommutative Gr\'{o}bner Basis on Quiver Algebras
| Autor: | Waweru, Daniel K., Maingi, Damian M |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Springer Proceedings in Mathematics & Statistics, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-031-32009-5_30 |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
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