习题 5, § 3

令 A 为交换代数，令 S 为生成的 A 的子集作为 K-代数。 假设$\operatorname{Card}(S) < \operatorname{Card}(K)$。 Show that if $\mathfrak{M}$ is a maximal ideal of A, then the field $A/\mathfrak{M}$ is an algebraic extension of K. (Use Ex. 15 of V, p. 174 when $\operatorname{Card}(K) \leq \operatorname{Card}(N)$ and Ex. 4 when

Deduce that $A/\mathfrak{M} = K$ when K is algebraically closed.