Vol. 68, No. 1, 1977

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ISSN: 0030-8730
Generalized primitive elements for transcendental field extensions

James K. Deveney

Vol. 68 (1977), No. 1, 41–45

Let L be a finitely generated separable extension of a field K of characteristic p0. Artin’s theorem of a primitive element states that if L is algebraic over K, then L is a simple extension of K. If L is non-algebraic over K, then an element 𝜃 L with the property L = L(𝜃) for every L, L L′⊇ K, such that L is separable algebraic over Lis called a generalized primitive element for L over K. The main result states that if [K : Kp] > p, then there exists a generalized primitive element for L over K. An example is given showing that if [K : Kρ] p, then L need not have a generalized primitive element over K.

Mathematical Subject Classification 2000
Primary: 12F20
Received: 20 January 1976
Published: 1 January 1977
James K. Deveney