Abstract
A universal Grobner basis is a finite basis for a polynomial ideal that has the Grobner property with respect to all admissible term-orders. Let R be a commutative polynomial ring over a field K, or more generally a non-commutative polynomial ring of solvable type over K (see [KRW]). We show, how to construct and characterize left, right, two-sided, and reduced universal Grobner bases in R. Moreover, we extend the upper complexity bounds in [We4] to the construction of universal Grobner bases. Finally, we prove the stability of universal Grobner bases under specialization of coefficients. All these results have counterparts for polynomial rings over commutative regular rings (comp. [We3]).
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