Module theory MOC

Reducibility of modules

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

#state/tidy | #lang/en | #SemBr