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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.
JournalJournal of Symbolic Computation
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Translation No
Refereed No