Abstract
One of the first and most fundamental results in the theory of non-algebraic field extensions is Lüroth’s theorem (1876): If k ⊂ L ⊆ k(t) = K are field extensions, with t transcendental over k, then there exists u ε L such that L = k(u).
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Ohm, J. (1994). Function Fields of Conies, a Theorem of Amitsur—MacRae, and a Problem of Zariski. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_21
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