Corollary 1

Tag 04QE, permanent. Cite it as [Bourbaki, Tag 04QE].

Commutative Algebra, chapter V, § 2. The lift of prime ideals

Under the hypotheses of Proposition 6, let f be a homomorphism from A to a field L and g1, g_2 two homomorphisms from A' to L which extend f. Then there exists a K-automorphism $\sigma \in K'$ such that $g_1 = g_2 \circ \sigma$ .*

The proof starting from Proposition 6 is the same as that of the Corollary to Theorem 2 starting from the latter.

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

Cited by

Proposition 7, § 8

Cites

Corollary to Theorem 2
Proposition 6