In mathematics, particularly in algebra, a field extension is a pair of fields E ⊆ F, {\displaystyle E\subseteq F,} such that the operations of E are those of F restricted to E. In this case, F is an extension field of E and E is a subfield of F. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Wikipedia