2004/09/28 by Frederick Leitner, Leitner, Frederick, Robert Pawloski +1
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.RA #msc:13P10 #msc:16Z05
paper · pdf · doi:10.48550/arxiv.math/0409565
10 pages
arxiv created 2004/10/14 · arxiv updated 2009/12/01
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.