On the finiteness of Gröbner bases computation in quotients of the free algebra

Summary, in English

We investigate, for quotients of the non-commutative polynomial

ring, a property that implies finiteness of Gröbner bases

computation, and examine its connection with Noetherianity.

We propose a Gröbner bases theory for our factor algebras, of particular interest for

one-sided ideals, and show a few

applications, e.g. how to compute (one-sided) syzygy modules.

• Author: Patrik Nordbeck
• Department/s: Mathematics (Faculty of Engineering); Algebra
• Publishing year: 2001
• Language: English
• Pages: 157-180
• Publication/Series: Applicable Algebra in Engineering, Communication and Computing
• Volume: 11
• Issue: 3
• Links: http://www.springerlink.com/content/mlwe4gqth788yd6h/fulltext.pdf; http://dx.doi.org/10.1007/s002000000045
• Document type: Journal article
• Publisher: Springer
• Topic: Mathematics
• Keywords: non-commutative algebras; Grobner bases; Dickson's lemma; Noetherianity; syzygies; POLYNOMIAL-RINGS
• Status: Published
• Research group: Algebra
• ISBN/ISSN/Other: ISSN: 1432-0622