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TitleSome results on Gröbner bases over commutative rings
Author(s) William W. Adams, Ann K. Boyle
TypeArticle in Journal
AbstractLet F be a finite set of polynomials in A[x], where A is a commutative ring and x is a single variable. This paper is concerned with what properties are imposed on the coefficients of these polynomials if F is assumed to be a Grobner basis. When A=R[y] a polynomial ring in n variables over some commutative ring R, we characterize Grobner bases in R [y,x] in terms of Grobner bases in R[y][x] and Grobner bases in R[y]. We then address the question of lifting Grobner bases from A to A[x] by examining the relationship between Szekeres bases and Grobner bases. Finally we show that if A is a UFD, then, if the elements of F form a Grobner basis and are relatively prime, the same is true of the leading coefficients of the polynomials in F.
ISSN0747-7171
LanguageEnglish
JournalJournal of Symbolic Computation
Volume13
Number5
Pages473-484
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year1992
MonthMay
Translation No
Refereed No
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