I saw the two properties mentioned by the post on
With intuition I think if $M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 \cap M_2 = 0$ implies M is isomorphic to $M_1 \oplus M_2$, but I did not find this in books I could find. Is this true?