Comprehensive Grobner bases and von Neumann regular rings (CGB特集)
Katsusuke Nabeshima · 数式処理 · 2007
There is a close relation between comprehensive Grobner bases and non-parametric Grobner bases over commutative von Neumann regular rings. By this relation, Grobner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Grobner bases. (Therefore, this Grobner basis is called an “alternative comprehensive Grobner basis (ACGB)”.) In the first part of this paper, we treat the theory of Grobner bases in polynomial rings over a commutative von Neumann regular ring. In the second part, we describe the special type of comprehensive Grobner bases which is called alternative comprehensive Grobner bases on varieties (ACGB-V).