An alternative approach to comprehensive Gröbner bases
Akira Suzuki, Yosuke Sato · 2002
We give an alternative definition of comprehensive Gröbner bases in terms of Gröbner bases in polynomial rings over commutative Von Neumann regular rings. Our comprehensive Gröbner bases are defined as Gröbner bases in polynomial rings over certain commutative Von Neumann regular rings, hence they have two important properties which do not hold in standard comprehensive Gröbner bases. One is that they have canonical forms. Another one is that we can define monomial reductions which are compatible with any instantiation.