In mathematics, Lüroth's theorem asserts that every field that lies between a field K and the rational function fieldK(X) must be generated as an extension of K by a single element of K(X). This result is named after Jacob Lüroth, who proved it in 1876.[1]
Statement
Let be a field and be an intermediate field between and , for some indeterminate X. Then there exists a rational function such that . In other words, every
intermediate extension between and is a simple extension.