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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/2320

Title: Strong Gröbner bases for polynomials over a principal ideal ring
Authors: Norton, G.H.
Salagean, A.M.
Issue Date: 2001
Publisher: © Australian Mathematical Society
Citation: NORTON, G.H. and SALAGEAN, A.M. 2001. Strong Gröbner bases for polynomials over a principal ideal ring. Bulletin of the Australian Mathematical Society, 64, pp. 505-528
Abstract: Gröbner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Gröbner bases, also known as D-bases. Several authors have shown that strong Gröbner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring: we characterise Gröbner bases and strong Gröbner bases when A is a principal ideal ring. We also give algorithms for computing Gröbner bases and strong Gröbner bases which generalise known algorithms to principal ideal rings.In particular, we give an algorithm for computing a strong Gröbner basis over a finite-chain ring, for example a Galois ring.
Description: This article was published in the journal, Bulletin of the Australian Mathematical Society [© Australian Mathematical Society]
URI: https://dspace.lboro.ac.uk/2134/2320
ISSN: 0004-9727
Appears in Collections:Published Articles (Computer Science)

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