Definition 1

Tag 0040, permanent. Cite it as [Bourbaki, Tag 0040].

Algebra, VIII, p. 55, § 4. Semisimple Modules

A module is called semisimple if it is the direct sum of a family of simple modules.[^1].

A multimodule is called semisimple if it is the direct sum of a family of simple multimodules (cf. I, §4, No. 4, p. 37, Definition 7).

An A-module M is semisimple if and only if it is semisimple when viewed as a module over its ring of homotheties $A_M$ .

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

Example 1, § 2

Cites

I, §4, No. 4, p. 37, Definition 7 not in this corpus