Galois theory

== English == === Etymology === Standardly constructed calque of French théorie de Galois (which was used as a section heading in 1870, Camille Jordan, Traité des substitutions et des équations algébriques). First appeared in print in 1893, Bulletin of the New York Mathematical Society. Ultimately, named after French mathematician Evariste Galois (1811-1832), who first developed the theory to explore how the roots of a given polynomial equation relate to each other. === Pronunciation === IPA(key): /ˈɡælwɑ ˈθi.əɹi/ === Noun === Galois theory (usually uncountable, plural Galois theories) (algebra, field theory) 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. 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. ==== Translations ==== === References === === Further reading === Galois group on Wikipedia.Wikipedia Galois field on Wikipedia.Wikipedia Differential Galois theory on Wikipedia.Wikipedia Grothendieck's Galois theory on Wikipedia.Wikipedia Galois connection on Wikipedia.Wikipedia Galois theory on Encyclopedia of Mathematics Galois theory of rings on Encyclopedia of Mathematics Galois Theory on Wolfram MathWorld