Let $R$ be a commutative DVR, and let $M$ be the free $R$-module of finite rank $k\ge 2$. Let $N$ be a submodule of $M$ isomorphic to $R$.
Is it true that $N$ is a direct summand of $M$?
Thanks in advance.
Let $R$ be a commutative DVR, and let $M$ be the free $R$-module of finite rank $k\ge 2$. Let $N$ be a submodule of $M$ isomorphic to $R$.
Is it true that $N$ is a direct summand of $M$?
Thanks in advance.