Field extension

A field extension formula_1 is a field containing a given field formula_2 as a subfield. 
The notation formula_3 means that formula_1 is an extension of the field formula_2.
formula_1 is sometimes called an overfield of the field formula_2.
Algebraic over formula_2.
An element of the field formula_1 is called algebraic over formula_2 if it satisfies some algebraic equation with coefficients in formula_2, and transcendental otherwise.