One-sided Noncommutative Groebner Bases with Applications to Green's Relations
Anne Heyworth · arXiv (Cornell University) · 1999
Standard noncommutative Gröbner basis procedures are used for computing ideals of free noncommutative polynomial rings over fields. This paper describes Gröbner basis procedures for one-sided ideals in finitely presented noncommutative algebras over fields. The polynomials defining a $K$-algebra $A$ as a quotient of a free $K$-algebra are combined with the polynomials defining a one-sided ideal $I$ of $A$, by using a tagging notation. Standard noncommutative Gröbner basis techniques can then be applied to the mixed set of polynomials, thus calculating $A/I$ whilst working in a free structure, avoiding the complication of computing in $A$. The paper concludes by showing how the results can be applied to completable presentations of semigroups and so enable calculations of Green's relations.