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In algebra, a subfield of an algebra A over a field F is an F-subalgebra that is also a field. A maximal subfield is a subfield that is not contained in a strictly larger subfield of A.
If A is a finite-dimensional central simple algebra, then a subfield E of A is called a strictly maximal subfield if .
![{\displaystyle [E:F]=(\dim _{F}A)^{1/2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f66c435c0b5b5e815dcd175d9b0f8fd8b1a6ca6)
References
edit- Richard S. Pierce. Associative algebras. Graduate texts in mathematics, Vol. 88, Springer-Verlag, 1982, ISBN 978-0-387-90693-5
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