Subfield of an algebra explained

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. Associative algebras. Graduate texts in mathematics, Vol. 88, Springer-Verlag, 1982,