Accession Number:

ADP006605

Title:

Using Groebner Bases to Determine the Nature of Field Extensions,

Descriptive Note:

Corporate Author:

CORNELL UNIV ITHACA NY

Personal Author(s):

Report Date:

1992-03-01

Pagination or Media Count:

3.0

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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE