Let $M$ be an $R$ module. Is this true for start a proof that we say "Let $S$ denote the indecomposable summands of $M$"?
In fact,
I want to know whether any module over a Dedekind domain (or a DVR) has an indecomposable summand.
Thanks.
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user26857
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S Ali Mousavi
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It is not true for start to say "Let S denote the indecomposable summands of M" since we dont know if S is empty or not? – user 1 Feb 28 '15 at 12:57
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Does each module has idecomposable decomposition? – S Ali Mousavi Feb 28 '15 at 14:03
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Any finitely generated module over a Dedekind domain is the direct sum of indecomposable modules. – Mohan Jun 26 '15 at 01:59