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Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings

Francis, Maria and Dukkipati, Ambedkar (2014) Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings. In: JOURNAL OF SYMBOLIC COMPUTATION, 65 . pp. 1-14.

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Official URL: http://dx.doi.org/10.1016/j.jsc.2014.01.001

Abstract

In this paper, we extend the characterization of Zx]/(f), where f is an element of Zx] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us to extend the Grobner basis method of computing a k-vector space basis of residue class polynomial rings over a field k (Macaulay-Buchberger Basis Theorem) to rings, i.e. Ax(1), ... , x(n)]/a, where a subset of Ax(1), ... , x(n)] is an ideal. We give some insights into the characterization for two special cases, when A = Z and A = ktheta(1), ... , theta(m)]. As an application of this characterization, we show that the concept of Border bases can be extended to rings when the corresponding residue class ring is a finitely generated, free A-module. (C) 2014 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, ENGLAND
Keywords: Macaulay Basis Theorem; Reduced Grobner basis for rings
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 03 Jun 2014 08:34
Last Modified: 03 Jun 2014 08:34
URI: http://eprints.iisc.ac.in/id/eprint/49111

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