Sentence:  Let us describe in general the <WSD>subfield</WSD> "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) \qquad f(c) = a_0 + a_1 c + a_2 c^2 + ... + a_n c^n \qquad \qquad \mbox{(each } a_i \mbox{ in } F\mbox{).}/ [...]/    If "f"("c") and "g"("c") &ne; 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 <WSD>subfield</WSD>; it is the field "generated" by "F" and "c" and is conventionally denoted by "F"("c"), with "round" brackets. 
Meaning of the word marked with <WSD> tags:  A subring of a field, containing the multiplicative identity and closed under inversion.