Galois theory

English Etymology Standardly constructed calque of en fr 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.Earliest Known Uses of Some of the Words of Mathematics (G) 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 en /ˈɡælwɑ ˈθi.əɹi/ Noun - + en 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. en 1989 G. Karpilovsky Topics in Field Theory North-Holland https://books.google.com.au/books?id=-2WR0fw9gLMC&pg=PA299&dq=%22Galois+theory%22%7C%22Galois+theories%22&hl=en&sa=X&ved=0ahUKEwiG3-uOmPvcAhWTxIMKHTgcCFI4ZBDoAQi_AjA2#v=onepage&q=%22Galois%20theory%22%7C%22Galois%20theories%22&f=false 299 In this chapter we present the Galois theory which may be described as the analysis of field extensions by means of automorphism groups. en 1989 Donald S. Passman Infinite Crossed Products https://books.google.com.au/books?id=Rvy7I_j6DSIC&pg=PA297&dq=%22Galois+theory%22%7C%22Galois+theories%22&hl=en&sa=X&ved=0ahUKEwiG3-uOmPvcAhWTxIMKHTgcCFI4ZBDoAQi1ATAe#v=onepage&q=%22Galois%20theory%22%7C%22Galois%20theories%22&f=false 297 Academic Press 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. en 2003 Introduction Leila Schneps Galois Groups and Fundamental Groups w:Cambridge University Press https://books.google.com.au/books?id=n1KIVYYQNH0C&pg=PR9&dq=%22Galois+theory%22%7C%22Galois+theories%22&hl=en&sa=X&ved=0ahUKEwiG3-uOmPvcAhWTxIMKHTgcCFI4ZBDoAQi6ATAf#v=onepage&q=%22Galois%20theory%22%7C%22Galois%20theories%22&f=false ix 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. Translations branch of mathematics French: fr théorie de Galois f German: de Galoistheorie f Italian: it teoria di Galois f Polish: pl teoria Galois f References Further reading Galois group Galois field Differential Galois theory Grothendieck's Galois theory Galois connection Galois theory on Encyclopedia of Mathematics Galois theory of rings on Encyclopedia of Mathematics Galois Theory on MathWorld Wolfram MathWorld en eponyms