Remark 111.16.2. Let k be a field. Then for every integer n\in {\mathbf N} and every maximal ideal {\mathfrak m} \subset k[x_1, \ldots , x_ n] the quotient k[x_1, \ldots , x_ n]/{\mathfrak m} is a finite field extension of k. This will be shown later in the course. Of course (please check this) it implies a similar statement for maximal ideals of finitely generated k-algebras. The exercise above proves it in the case k = {\mathbf C}.
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