Using Groebner Bases to Determine the Nature of Field Extensions,

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.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1992
Accession Number
ADP006605

Entities

People

  • Moss E. Sweedler

Organizations

  • Cornell University

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Continents
  • Mathematics
  • Minnesota
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.