One-Sided Noncommutative Gröbner Bases with Applications to Computing Green's Relations

✍ Scribed by Anne Heyworth

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 125 KB
• Volume: 242
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8801

✦ Synopsis

Standard noncommutative Grobner basis procedures are used for computing ïdeals of free noncommutative polynomial rings over fields. This paper describes Grobner basis procedures for one-sided ideals in finitely presented noncommuta-ẗive 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 whose essential effect is to forbid left multiplication. Standard noncommutative Grobner basis techniques can then be applied to the mixed set of polynomials, thus calculating ArI 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.