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TitleGr\"obner bases on algebras based on well-ordered semigroups.
Author(s) Yuji Kobayashi
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe develop the theory of Gröbner bases on an algebra based on a well-ordered 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 well-order, 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. 1,610). 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 so-called critical pair theorem. We need to consider z-elements as well as usual critical pairs come from overlapping applications of rules.

KeywordsGröbner basis; well-ordered semigroup; rewriting system; critical pair; z-element
ISBN978-981-4317-60-3/hbk; 978-981
URL http://www.worldscientific.com/doi/10.1142/9789814317610_0007
PublisherHackensack, NJ: World Scientific
Translation No
Refereed No