Remark 3

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

Algebra, VIII, p. 191, § 11. Grothendieck Groups

Let E be an A-module of finite length. By c), there exists a semisimple A-module $E'$ of finite length such that $[E] = [E']$ , and by b), such a module is defined up to an isomorphism; we sometimes call it a semisimplification of E.

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.

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