I have an $R$-module $M$ with $R$ an integral domain. The localizatiom $(tM)_P$ of the torsion submodule of $M$ is a summand of $M_P$ for each maximal ideal $P.$ Does it follow that $tM$ is a summand of $M?$ Part of me wants to say yes, but part of me says maybe not. Any help or suggestions would be appreciated.
2026-03-27 10:45:52.1774608352
Does locally a summand imply summand?
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