Editing Algebraic function field (section)

==Example==
As an example, in the [[polynomial ring]] ''k''{{space|hair}}[''X'',''Y''] consider the [[ideal (ring theory)|ideal]] generated by the [[irreducible polynomial]] ''Y''<sup>{{space|hair}}2</sup>&thinsp;−&thinsp;''X''<sup>{{space|hair}}3</sup> and form the [[field of fractions]] of the [[quotient ring]] ''k''{{space|hair}}[''X'',''Y'']/(''Y''<sup>{{space|hair}}2</sup>&thinsp;−&thinsp;''X''<sup>{{space|hair}}3</sup>). This is a function field of one variable over ''k''; it can also be written as <math>k(X)(\sqrt{X^3})</math> (with degree 2 over <math>k(X)</math>) or as <math>k(Y)(\sqrt[3]{Y^2})</math> (with degree 3 over <math>k(Y)</math>). We see that the degree of an algebraic function field is not a well-defined notion.