Exercise 4, § 3

Algebra, V, p. 147

Let F be a transcendental extension of a field E. Show that

[F : E] \geq \operatorname{Sup}(\operatorname{Card}(E), \operatorname{Card}(N))

with equality if the extension F can be generated by a countable family of elements. (Use Ex. 7 of IV, p. 89.)

Solution

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