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Buchberger-Zacharias theory of multivariate Ore extensions. (English) Zbl 1379.16025

Summary: Following the recent survey on Buchberger-Zacharias Theory for monoid rings \(R [\mathsf{S}]\) over a unitary effective ring \(R\) and an effective monoid \(\mathsf{S}\), we propose here a presentation of Buchberger-Zacharias Theory and related Gröbner basis computation algorithms for multivariate Ore extensions of rings presented as modules over a principal ideal domain, using Möller-Pritchard lifting theorem.

MSC:

16U20 Ore rings, multiplicative sets, Ore localization
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
20M25 Semigroup rings, multiplicative semigroups of rings

Software:

Letterplace; Plural
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Full Text: DOI

References:

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