Constructing fields within a bigger field Fields can be constructed inside a given bigger container field. Suppose given a field , and a field containing as a subfield. For any element of , there is a smallest subfield of containing and , called the subfield of F generated by and denoted . The passage from to is referred to by adjoining an element to . More generally, for a subset , there is a minimal subfield of containing and , denoted by .
constructing fields within a bigger field fields can be constructed inside a given bigger container field suppose given a field  and a field containing as a subfield for any element of  there is a smallest subfield of containing and  called the subfield of f generated by and denoted  the passage from to is referred to by adjoining an element to  more generally for a subset  there is a minimal subfield of containing and  denoted by 