Problem of Krull-Schmidt-Remak-Azumaya-Matlis

He also observed that in case B is noetherian, the answer is in the affirmative. In [2], Faith and Walker have shown that the answer is in the affirmative in case M is injective. As shown by Jean-Yves Chamard [1], the answer is again in the affirmative if M satisfied the condition: the intersection of two complemented submodules of M is again a complemented submodule of M.