cyclic algebra
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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.|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}}
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