doi: 10.17706/ijapm.2017.7.4.224-240
Syzygies on Path Algebras
,
Andre Saint Eudes Mialebama Bouesso
2
- 1 Université D’Abomey-Calavi, Département De Mathématiques, 01 Bp 4521, Cotonou 01, Bénin.
- 2 Stellenbosch University, African Institute For Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa
Abstract
Let <em>K</em> be a field and <em>KQ</em> be a noetherian path algebra for the quiver Q. Given a left (resp. right) finitely generated ideal<em> I </em>of <em>KQ</em>, we propose a new idea for computing left (resp. right) Groebner bases on <em>KQ</em>. As application, we propose a method for computing the so called left (resp. right) syzygies, that is, given polynomials <em>f</em><sub>1</sub>,...,<em>f<sub>s</sub></em> ∈<em>KQ</em> \{0} we propose a method for computing the set of all elements (<em>h</em><sub>1</sub>,...,<em>h<sub>s</sub></em>)∈(<em>KQ</em>)<sup><em>s</em></sup> such that <em>h</em><sub>1</sub><em>f</em><sub>1</sub> + ... + <em>h<sub>s</sub>f<sub>s</sub></em> = 0 (resp. <em>f</em><sub>1</sub><em>h</em><sub>1</sub> + ... + <em>f<sub>s</sub>h<sub>s</sub></em> = 0).
Keywords
- Groebner bases
- path algebra
- syzygies
How to Cite
Sylvain Attan and Andre Saint Eudes Mialebama Bouesso, "Syzygies on Path Algebras," International Journal of Applied Physics and Mathematics, vol. 7, no. 4, pp. 224-240, 2017. https://doi.org/ 10.17706/ijapm.2017.7.4.224-240
Copyright & License
Copyright © 2017 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).