|Title||Gröbner Bases for Polynomial Ideals over Commutative Noetherian Rings and
|Author(s)|| Leo Bachmair, Ashish Tiwari|
|Type||Technical Report, Misc|
|Abstract||We present a completion-like procedure for constructing weak and strong Grobner bases for polynomial ideals over commutative Noetherian rings with unit. This generalizes all the known algorithms for computing Grobner bases for polynomial ideals over various different coefficient domains. The coefficient domain is incorporated using constraints. Constraints allow us to describe an optimized procedure for computing Grobner bases. The optimization restricts the number of superpositions that need to be considered. Weak Grobner bases are shown to extend to Grobner bases under an additional ordering assumption on coefficient domain. The conditions on the coefficient domain are the weakest possible and are shown to carry over from ring B to B[X],|
thus giving a hierarchic algorithm for construction of Grobner bases.