Unital Grobner Bases over Arbitrary Ground Rings

Details Unital Grobner Bases over Arbitrary Ground Rings Unital Grobner Bases over Arbitrary Ground Rings

2004-09-28

arxiv.org/abs/math/0409565v2

Mathematics

Rings and Algebras

10 pages

Scientific paper

Let R be a commutative ring with unity and a let A be a not necessarily commutative R-algebra which is free as an R-module. If I is an ideal in A, one can ask when A/I is also free as an R-module. We show that if A has an admissible system and I has a unital Grobner basis then A/I is free as an R-module. We prove a version of Buchberger's theorem over R and, as a corollary, we obtain a Grobner basis proof of the Poincare-Birkhoff-Witt Theorem over a commutative ground ring.

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