An alternative approach to comprehensive Grbner bases
We give an alternative definition of comprehensive Grbner bases in terms of Grbner bases in polynomial rings over commutative Von Neumann regular rings. Our comprehensive Grbner bases are defined as Grbner bases in polynomial rings over certain commutative Von Neumann regular rings, hence they have two important properties which do not hold in standard comprehensive Grbner bases. One is that they have canonical forms in a natural way. Another one is that we can define monomial reductions which are compatible with any instantiation. Our comprehensive Grbner bases are wider than Weispfennings original comprehensive Grbner bases. That is there exists a polynomial ideal generated by our comprehensive Grbner basis which cannot be generated by any of Weispfennings original comprehensive Grbner bases.
13b25 13p10 68w30