simple module

《Abstract Algebra》 · 第 847 页 · Section 18.1「Linear Actions and Modules over Group Rings」，Definition (1)

Let $R$ be a ring and let $M$ be a nonzero $R$-module. The module $M$ is said to be irreducible (or simple) if its only submodules are $0$ and $M$; otherwise $M$ is called reducible.