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.