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,...,f_s ∈KQ \{0} we propose a method for computing the set of all elements (h₁,...,h_s)∈(KQ)^s such that h₁f₁ + ... + h_sf_s = 0 (resp. f₁h₁ + ... + f_sh_s = 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.