Proposition 2
Tag 004F, permanent. Cite it as [Bourbaki, Tag 004F].
Algebra, VIII, p. 61, § 4. Semisimple Modules
If a module is the sum of isotypical submodules of type S, then it is isotypical of type S. The submodules and the quotient modules of an isotypical module of type S are isotypical of type S.
The first assertion follows from the definitions, the second from Corollary 3 of VIII, p. 56.
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 2, § 12
- Definition 4, § 4
- Theorem 2, § 4
- Proposition 1, § 7
- lie-i-s3-prop-12 not in this corpus