Cyclic algebra

{{inline |date=May 2024}} In algebra, a '''cyclic division algebra''' is one of the basic examples of a division algebra over a field and plays a key role in the theory of central simple algebras.

== Definition == Let ''A'' be a finite-dimensional central simple algebra over a field ''F''. Then ''A'' is said to be '''cyclic''' if it contains a strictly maximal subfield ''E'' such that ''E''/''F'' is a cyclic field extension (i.e., the Galois group is a cyclic group).

== See also == * {{slink|Factor system#Cyclic algebras}}{{snd}}cyclic algebras described by factor systems. * {{slink|Brauer group#Cyclic algebras}}{{snd}}cyclic algebras are representative of Brauer classes.

== References == * {{cite book|last=Pierce|first=Richard S.|author-link=Richard S. Pierce|title=Associative Algebras|publisher=Springer-Verlag|year=1982|isbn=978-0-387-90693-5|series=Graduate Texts in Mathematics, volume 88|oclc=249353240|url-access=registration|url=https://archive.org/details/associativealgeb00pier_0}} * {{cite book|last=Weil|first=André|author-link=André Weil|title=Basic Number Theory|edition=third|publisher=Springer|year=1995|isbn=978-3-540-58655-5|oclc=32381827}}

Category:Algebras Category:Ring theory

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