Meaning of Galois theory | Babel Free

Definitions

The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations. It provides a link between field theory and group theory: it permits certain problems in the former to be reduced to the latter, which in some respects is simpler and better understood.

uncountable, usually

Equivalents

Examples

“In this chapter we present⟳ the Galois theory which may be described as the analysis of field extensions by means of automorphism groups.”

“The Galois theory of noncommutative rings is a natural outgrowth of the Galois theory of fields.”

“1992, Journal of Contemporary Mathematical Analysis, Volume 27, Allerton Press⟳, page 4, Though often our results are prompted by the classical or parallel Galois theories, their proofs are completely different and are based on the set-theoretical approach⟳.”

“Classical Galois theory has developed a number⟳ of extensions and ramifications into more specific theories, which combine⟳ it with other areas of mathematics or restate its main problems in different situations. Three of the most important are geometric Galois theory, differential Galois theory, and Lie⟳ Galois theory, all of which have⟳ undergone very rapid development in recent years.”

CEFR level