Module theory MOC

Reducibility of modules

Let 𝑀 be a (left) 𝑅-module. We say that 𝑀 is

• simple or irreducible iff it has no nonzero proper submodule;
• semisimple or completely reducible iff it is the direct sum of simple modules;
• decomposable iff it is the direct sum of two nonzero modules;
• indecomposable iff it is not decomposable.

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