Simple module

Summary

A simple module is a nonzero module whose only submodules are zero and the module itself. Simple modules are the building blocks of modules of finite length: the factors of a composition series are simple. Over a group algebra, simple modules are the same as irreducible representations. Every simple left module over a ring $R$ is isomorphic to $R/\mathfrak{m}$ for a maximal left ideal $\mathfrak{m}$.