Corollary (Schur’s lemma)

Tag 00RZ, permanent. Cite it as [Bourbaki, Tag 00RZ].

Algebra, VIII, p. 47, § 3. Simple Modules

The endomorphism ring of a simple module is a field.

If M is a simple A-module, then every nonzero element of the nonzero ring End $_A(M)$ is invertible (Proposition 2, c)), so End $_A(M)$ is a field.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Theorem 1, § 3
Corollary 4, § 4

Cites

Proposition 2