Details:
Title  Transitivity for weak and strong Gröbner bases  Author(s)  William W. Adams, Ann K. Boyle, Philippe Loustaunau  Type  Article in Journal  Abstract  Let 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 Ggraded ring R$ for which every ideal has a strong Grobner basis is isomorphic to k[x_1,...,x_n], where k is a PID.  Length  17  ISSN  07477171 
File 
 Language  English  Journal  Journal of Symbolic Computation  Volume  15  Number  1  Pages  4965  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  1993  Month  January  Translation 
No  Refereed 
No 
