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