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I thought the question was about extensions of finite fields before opening the link.

edited Sep 29, 2009 at 14:55

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Finite Extension of Fields with no Primitive Element

What is an example of a finite field extension which is not generated by a single element?

Background: A finite field extension E of F is generated by a primitive element if and only if there are a finite number of intermediate extensions. See, for example, [Lang's Algebra, chapter V, Theorem 4.6].

asked Sep 28, 2009 at 23:40

Anton Geraschenko