Two applications of noncommutative Groebner bases

Abstract

In this paper, by using the noncommutative Groebner bases in the sense of Mora, we first give an algorithmic description of the defining relations of a quadric algebra with a PBW basis, which enables us to use Berger’sq-Jacobi condition in a more general extent; and secondly, we give an algorithmic determination of the defining relations of the associated graded algebras of a given algebra with given defining relations.