Galois theory

plural Galois theories

1. uncountableusuallyfield theoryalgebraThe 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.

   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.

   3 more examples

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

   1989, G. Karpilovsky, Topics in Field Theory, North-Holland, page 299

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

   1989, Donald S. Passman, Infinite Crossed Products, Academic Press, page 297

   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.

   2003, “Introduction”, in Leila Schneps, editor, Galois Groups and Fundamental Groups, Cambridge University Press, page ix