Title  Gr\"obner bases on algebras based on wellordered semigroups. 
Author(s)  Yuji Kobayashi 
Type  Book, Chapter in Book, Conference Proceeding 
Abstract  We develop the theory of Gröbner bases on an algebra based on a wellordered semigroup inspired by the discussions in Farkas et al.,3,4 where the authors study multiplicative bases in an axiomatic way. We consider a reflexive semigroup with 0 equipped with a suitable wellorder, and use it as a base of an algebra over a commutative ring, on which we develop a Gröbner basis theory.
Our framework is considered to be fairly general and unifies the existing Gröbner basis theories on several types of algebras (ref. 1,6–10). We discuss a Gröbner basis theory from a view point of rewriting systems. We study behaviors of critical pairs in our situation and give a socalled critical pair theorem. We need to consider zelements as well as usual critical pairs come from overlapping applications of rules.

Keywords  Gröbner basis; wellordered semigroup; rewriting system; critical pair; zelement 
ISBN  9789814317603/hbk; 978981 
URL 
http://www.worldscientific.com/doi/10.1142/9789814317610_0007 
Language  English 
Pages  85102 
Publisher  Hackensack, NJ: World Scientific 
Year  2010 
Edition  0 
Translation 
No 
Refereed 
No 