Definition 1

Let $\pi$ be an irreducible element of a principal ideal domain A; an A-module M is called rr-primary if, for all $x \in M$, there exists an integer $n \geq 1$ such that $\pi^n x = 0$ (in other words, if M is equal to the submodule $M_\pi$).

Clearly every cyclic module of the form $A/(\pi^s)$ is rr-primary. For an arbitrary A-module M, the submodule $M_\pi$ is rr-primary.