subfield

A smaller, more specialized area of study or occupation within a larger one

A subring of a field, containing the multiplicative identity and closed under inversion.

• Let us describe in general the subfield generated by a given element. Let K be a given field, F a subfield of K, and c an element of K. Consider those elements of K which are given by polynomial expressions of the form (1)#92;qquadf(c)#61;a
• We are now in a position to describe the subfield of K generated by F and our algebraic element u. This subfield F(u) clearly contains the subdomain F[u] of all elements expressible as polynomials f(u) with coefficients in F (cf. (1)). Actu