Subfield of an algebra

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

References

• Richard S. Pierce (1982) Associative Algebras, Graduate Texts in Mathematics Vol. 88, Springer-Verlag ISBN 978-0-387-90693-5