FPM 1996, vol. 2, no. 2, pp. 501-509

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 2, PAGES 501-509

Gröbner bases and coherentness of monomial associative algebras

D. I. Piontkovsky

Abstract

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Let $A$ be an associative algebra which is defined by a finite number of monomial relations. In this paper we show that any finitely generated one-sided ideal in $A$ has a finite Gröbner basis. We propose an algorithm for constructing of this basis. As a consequence we obtain an algorithm for computation of syzygy module for the system of generators of the ideal. In particular, this syzygy module is finitely generated. It means that $A$ is coherent.

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