
Accession Number : ADP006605
Title : Using Groebner Bases to Determine the Nature of Field Extensions,
Corporate Author : CORNELL UNIV ITHACA NY
Personal Author(s) : Sweedler, Moss E.
Report Date : MAR 1992
Pagination or Media Count : 3
Abstract : Suppose the field of fractions of a polynomial ring modulo a prime ideal contains an element c and a finitely generated subfield K. Groebner basis techniques' are presented which determine if c is algebraic or transcendental over K. If c is algebraic over K, a minimal polynomial for c over K is found. The minimal polynomial tells whether c lies in K. What makes everything work is the reduction to questions about finitely generated algebras and the use of Buchberger theory with tag variables.
Descriptors : *POLYNOMIALS, *RINGS, REDUCTION, WORK, ALGEBRA, COMPUTATIONS.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE