Details:
Title  On lucky ideals for Gröbner basis computations  Author(s)  Franz Pauer  Type  Article in Journal  Abstract  Let R be a principal ideal ring (i.e. a commutative ring such that all ideals are principal; we do not assume that R is entire), R[x]: = R[x1, …, xn] the polynomial ring in n variables over R and I an ideal in R[x]. Intuitively, an ideal P ...; R is "lucky" for I, if we do not loose too much information on Gröbner bases of I, when we project I to Image. Let F be an ideal basis of I. Examples in Ebert (1983) show that the coefficients of F give no direct criterion to detect luckiness of P, even if R is a domain, K its quotient field and F a Gröbner basis of the ideal generated by F in K[x]. However, If we consider the Gröbner basis of the ideal generated by F in R[x], we get direct and full information about lucky ideals. The main objective of this article is to give a precise version of this observation. As an application, a short proof for the main result in Winkler (1988) is given.  ISSN  07477171 
URL 
dx.doi.org/10.1016/07477171(92)90018Y 
Language  English  Journal  Journal of Symbolic Computation  Volume  14  Number  5  Pages  471482  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  1992  Month  November  Edition  0  Translation 
No  Refereed 
No 
