Reduced Groebner Bases in Polynomial Rings over a Polynomial Ring

Katsusuke Nabeshima

doi:10.1007/s11786-008-0060-8

Reduced Groebner Bases in Polynomial Rings over a Polynomial Ring

Katsusuke Nabeshima

Research Institute for Symbolic Computation

Research output: Contribution to journal › Article › peer-review

Abstract

We define reduced Gr\"obner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gr\"obner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Groebner bases by these algorithms. In this paper we propose a new notion of reduced Groebner bases in polynomial rings over a polynomial ring and we show that every ideal has a unique reduced Groebner basis.

Original language	English
Pages (from-to)	587-599
Number of pages	13
Journal	Mathematics in Computer Science
Volume	2
Issue number	4
DOIs	https://doi.org/10.1007/s11786-008-0060-8
Publication status	Published - 2007

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

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10.1007/s11786-008-0060-8

Cite this

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abstract = "We define reduced Gr\textbackslash{}{"}obner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gr\textbackslash{}{"}obner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Groebner bases by these algorithms. In this paper we propose a new notion of reduced Groebner bases in polynomial rings over a polynomial ring and we show that every ideal has a unique reduced Groebner basis.",

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AB - We define reduced Gr\"obner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gr\"obner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Groebner bases by these algorithms. In this paper we propose a new notion of reduced Groebner bases in polynomial rings over a polynomial ring and we show that every ideal has a unique reduced Groebner basis.

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DO - 10.1007/s11786-008-0060-8

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JO - Mathematics in Computer Science

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Reduced Groebner Bases in Polynomial Rings over a Polynomial Ring

Abstract

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