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Gröbner bases and products of coefficient rings

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journal contribution
posted on 21.08.2006 by G.H. Norton, Ana Salagean
Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A[x1,..., xn] can be easily obtained by ’joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor.

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Citation

NORTON and SALAGEAN, 2002. Gröbner bases and products of coefficient rings. Bulletin of the Australian Mathematical Society, 65, pp. 147-154

Publisher

© Australian Mathematical Society

Publication date

2002

Notes

This article was published in the journal, Bulletin of the Australian Mathematical Society[© Australian Mathematical Society]

ISSN

0004-9727

Language

en

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