# properties of semisimple modules

Let $R$ be a ring. Recall that $R$-module $M$ is called iff $M$ is a direct sum of simple module.

The following are equivalent for $R$-module $M$:

1. 1.

$M$ is semisimple;

2. 2.

$M$ is generated by its simple submodules;

3. 3.

for every submodule $N\subseteq M$ there exists a submodule $N^{\prime}\subseteq M$ such that $M=N\oplus N^{\prime}$.

Title properties of semisimple modules PropertiesOfSemisimpleModules 2013-03-22 18:53:27 2013-03-22 18:53:27 joking (16130) joking (16130) 4 joking (16130) Theorem msc 16D60