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 ${\displaystyle [E:F]=(\dim _{F}A)^{1/2}}$.

References

• Richard S. Pierce. Associative algebras. Graduate texts in mathematics, Vol. 88, Springer-Verlag, 1982, ISBN 978-0-387-90693-5