Remark 1

Tag 06HV, permanent. Cite it as [Bourbaki, Tag 06HV].

Algebra, V, p. 18, § 3. Algebraic extensions

With the notation of Th. 2, $E = K[a_1, a_2, ..., a_n]$ and hence $E$ is isomorphic to a quotient $K[X_1, X_2, ..., X_m]/\mathfrak{a}$ ; since $E$ is a field, $a$ is a maximal ideal in $K[X_1, ..., X_m]$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Th. 2