Strong Grobner bases for polynomials over a principal ideal ring

Norton, G. H. and Salagean, A. (2001) Strong Grobner bases for polynomials over a principal ideal ring. Bulletin of The Australian Mathematical Society, 64 3: 505-528.


Author Norton, G. H.
Salagean, A.
Title Strong Grobner bases for polynomials over a principal ideal ring
Journal name Bulletin of The Australian Mathematical Society   Check publisher's open access policy
ISSN 0004-9727
Publication date 2001-12
Sub-type Article (original research)
Volume 64
Issue 3
Start page 505
End page 528
Total pages 24
Editor M.G. Cowling
Place of publication Canberra
Publisher Austrtalian Mathematical Society
Collection year 2001
Language eng
Subject C1
230103 Rings And Algebras
780101 Mathematical sciences
0199 Other Mathematical Sciences
Abstract Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.
Keyword Mathematics
principal ideal ring
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Tue, 14 Aug 2007, 14:54:39 EST