# ra.rings and algebras – Representation theory terminology question

For a paper I’m writing, I need a term for a representation-theoretic concept that I’m sure someone has thought of before, so I thought I’d ask here rather than just make something up.

Let $$G$$ be a group and $$R$$ be a commutative ring. Consider an $$R(G)$$-module $$V$$. For any ideal $$I$$ of $$R$$, we have the submodule
$$I V = {text{c cdot v | c in I and v in V}}.$$
What is the term for $$R(G)$$-modules $$V$$ such that all submodules are of this form? The ones I’m interested in have the additional property that if you ignore the $$G$$-action, then they are free $$R$$-modules (though not finitely generated!), but I doubt this matters for this question.

For an easy example, if $$R = mathbb{Z}$$ and $$G = text{GL}(n,mathbb{mathbb{Z}})$$, then $$mathbb{Z}^n$$ has this property.

If $$R$$ is a field, then this reduces the the usual notion of an irreducible representation, so I think of this as a version of irreducibility. But looking through my ring-theory books, I can’t find it anywhere.