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 [ E : F ] = ( dim F A ) 1 / 2 {\displaystyle [E:F]=(\dim _{F}A)^{1/2}} .
References Richard S. Pierce (1982) Associative Algebras, Graduate Texts in Mathematics Vol. 88, Springer-Verlag ISBN 978-0-387-90693-5