An $R$-module $M$ is called Baer if for every $N\leq M_R$, ann$_{S}(N)$ is a direct summand of $S$ where $S=$ End$_{R}(M)$.
Question: Let $N$ and $K$ be Baer $R$-modules such that $N$ is isomorphic to a direct summand of $K$ and $K$ is isomorphic to a direct summand of $N$. Does $N\simeq K$? I am searching for a counterexample in this field.
Thank you for your comments.
