Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unital Grobner Bases over Arbitrary Ground Rings   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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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph