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Z-modules are the same as abelian groups, so a simple Z-module is an abelian group which has no non-zero proper subgroups.These are the cyclic groups of prime order.. If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.