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Gröbner bases and products of coefficient rings

Published online by Cambridge University Press:  17 April 2009

Graham H. Norton  and
Ana Sӑlӑgean
Graham H. Norton
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
Ana Sӑlӑgean
Affiliation:
Department of Computer Science, Loughborough University, Leicestershire LE11 3TUUnited Kingdom
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 145 - 152
Copyright
Copyright © Australian Mathematical Society 2002

References

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[3]Norton, G.H. and Sӑlӑgean, A., ‘Strong Gröbner bases for polynomials over a principal ideal ring’, Bull. Austral. Math. Soc. 64 (2001), 505–528.CrossRefGoogle Scholar
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