Simple modules

Let \(R\) be a ring. An \(R\)-module \(M\) is simple if \(M\neq 0\) and every submodule \(M' \leq M\) is either \(0\) or \(M\). A commutative ring \(R\) is simple if it is simple as an \(R\)-module, that is, if \(R\neq 0\) and its only ideals are \(0\) and \(R\).