Details:
Title  Some results on Gröbner bases over commutative rings  Author(s)  William W. Adams, Ann K. Boyle  Type  Article in Journal  Abstract  Let 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.  ISSN  07477171 
Language  English  Journal  Journal of Symbolic Computation  Volume  13  Number  5  Pages  473484  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  1992  Month  May  Translation 
No  Refereed 
No 
