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Strong Gröbner bases for polynomials over a principal ideal ring

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posted on 21.08.2006, 14:25 by G.H. Norton, Ana Salagean
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.

History

School

  • Science

Department

  • Computer Science

Pages

266160 bytes

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

Publisher

© Australian Mathematical Society

Publication date

2001

Notes

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

ISSN

0004-9727

Language

en

Exports

Loughborough Publications

Keywords

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