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TitleTransitivity for weak and strong Gröbner bases
Author(s) William W. Adams, Ann K. Boyle, Philippe Loustaunau
TypeArticle in Journal
AbstractLet R be a Noetherian integral domain which is graded by an ordered group G and let x be a set of n variables with a term order. It is shown that a finite subset F of R[x] is a weak (respectively strong) Grobner basis in R[x] graded by G x Z^n if and only if F is a weak Grobner basis in R[x] graded by {0} x Z^n and certain subsets of the set of leading coefficients of the elements of F form weak (respectively strong) Grobner bases in R. It is further shown that any G-graded ring R$ for which every ideal has a strong Grobner basis is isomorphic to k[x_1,...,x_n], where k is a PID.
Length17
ISSN0747-7171
File
LanguageEnglish
JournalJournal of Symbolic Computation
Volume15
Number1
Pages49-65
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year1993
MonthJanuary
Translation No
Refereed No
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