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