Subfield

"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#95;0#43;a#95;1c#43;a#95;2c²#43;...#43;a#95;ncⁿ#92;qquad#92;qquad#92;mbox#123;(each#125;a#95;i#92;mbox#123;in#125;F#92;mbox#123;).#125; [...] If f(c) and g(c) ≠ 0 are polynomial expressions like (1), their quotient f(c)/g(c) is an element of K, called a rational expression in c with coefficients in F. The set of all such quotients is a subfield; it is the field generated by F and c and is conventionally denoted by F(c), with round brackets."