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