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Analogs of Gröbner Bases in Polynomial Rings over a Ring

✍ Scribed by LYN J. MILLER

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
617 KB
Volume
21
Category
Article
ISSN
0747-7171

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✦ Synopsis

In this paper we will define analogs of Gröbner bases for R-subalgebras and their ideals in a polynomial ring R[x 1 , . . . , xn] where R is a noetherian integral domain with multiplicative identity and in which we can determine ideal membership and compute syzygies. The main goal is to present and verify algorithms for constructing these Gröbner basis counterparts. As an application, we will produce a method for computing generators for the first syzygy module of a subset of an R-subalgebra of R[x 1 , . . . , xn] where each coordinate of each syzygy must be an element of the subalgebra.

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