Using Groebner Bases to Determine the Nature of Field Extensions,
CORNELL UNIV ITHACA NY
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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.
- Numerical Mathematics