Remark 1

Tag 004K, permanent. Cite it as [Bourbaki, Tag 004K].

Algebra, VIII, p. 63, § 4. Semisimple Modules

Let M be an isotypical A-module of type S and $(V, \alpha )$ a description of M. Then M has finite length if and only if V is finite-dimensional, and in this case, we have the relation

long $_A(M) =$ dim $_D(V)$ .

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

Proposition 4, § 7

Cites

Nothing.