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 formula_1.