This article is cited in 9 papers

Gröbner bases and coherentness of monomial associative algebras

D. I. Piontkovskii


Abstract: 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.

UDC: 512.552.4

Received: 01.08.1995

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