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TitleOn lucky ideals for Gröbner basis computations
Author(s) Franz Pauer
TypeArticle in Journal
AbstractLet 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.
URL dx.doi.org/10.1016/0747-7171(92)90018-Y
JournalJournal of Symbolic Computation
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Translation No
Refereed No