Strictly maximal subfield

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

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