$M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 cap M_2 = 0$ implies M is...
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I saw the two properties mentioned by the post on Let $R$ be a ring, $M$ an $R$ -module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$ . Prove that $M/A cong B$ . 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?
modules direct-sum
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asked Nov 16 at 1:11
Eric Curtis
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