IJPAM: Volume 64, No. 4 (2010)

GRÖBNER BASES AND SYZYGIES ON MODULES
OVER ALGEBRAS BASED ON WELL-ORDERED
SEMIGROUPS

Yuji Kobayashi
Department of Information Science
Toho University
Funabashi, 274-8510, JAPAN
e-mail: [email protected]


Abstract.In our previous paper [#!Ko2!#] we have developed a Gröbner bases theory on algebras based on well-ordered semigroups. In this paper, we develop a theory of Gröbner bases on modules over such algebras. We give a critical pair theorem for rewriting systems on modules. It asserts that a system forms a Gröbner basis if all the critical pairs and $z$-elements are resolvable. We use it to compute syzygies on projective modules over our algebra. The results are applied to compute the intersections of submodules.

Received: August 23, 2010

AMS Subject Classification: 16S15, 16E05, 13P10, 68Q42, 68W30

Key Words and Phrases: Gröbner basis, well-ordered semigroup, rewriting system, syzygy, critical pair, $z$-element

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4