Exercise 7, § 3

Algebra, IV, p. 89

Let K be a commutative field. Show that

[K(T):K] = \operatorname{Sup}(\operatorname{Card}(K), \operatorname{Card}(N))

(Use the linear independence of the $1/(T - a)$ , $a \in K$ , to show that

[K(T) : K] \geq \operatorname{Card}(K)

)

Solution

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