Unital Grobner Bases over Arbitrary Ground Rings

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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.
10 pages

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Rings and Algebras, 16Z05; 13P10

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http://salesiana.dossiersoluciones.com/handle/123456789/72664

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409565
 http://arxiv.org/abs/math/0409565

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arXiv