Volume 7 Number 4 (Oct. 2017)
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IJAPM 2017 Vol.7(4): 224-240 ISSN: 2010-362X
doi: 10.17706/ijapm.2017.7.4.224-240

Syzygies on Path Algebras

Sylvain Attan, Andre Saint Eudes Mialebama Bouesso
Abstract—Let K be a field and KQ be a noetherian path algebra for the quiver Q. Given a left (resp. right) finitely generated ideal I of KQ, we propose a new idea for computing left (resp. right) Groebner bases on KQ. As application, we propose a method for computing the so called left (resp. right) syzygies, that is, given polynomials f1,...,fsKQ \{0} we propose a method for computing the set of all elements (h1,...,hs)∈(KQ)s such that h1f1 + ... + hsfs = 0 (resp. f1h1 + ... + fshs = 0).

Index Terms—Groebner bases, path algebra, syzygies.

Sylvain Attan is with Université D’Abomey-Calavi, Département De Mathématiques, 01 Bp 4521, Cotonou 01, Bénin.
Andre Saint Eudes Mialebama Bouesso is with Stellenbosch University, African Institute For Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa (email: MIALEBAMA@AIMS.AC.ZA).

Cite: Sylvain Attan, Andre Saint Eudes Mialebama Bouesso, "Syzygies on Path Algebras," International Journal of Applied Physics and Mathematics vol. 7, no. 4, pp. 224-240, 2017.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Nanowerk Database, Google Scholar, EBSCO, and ProQuest
E-mail: ijapm@iap.org
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