Let $\Bbb Z$ be the ring of integers and $I$ a non-countable index set. Why $$\prod_{i\in I} \Bbb Z$$ is not a projective $\Bbb Z$-module?
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Could this not follow from Kaplansky's Theorem for modules? – mathematics2x2life Dec 28 '13 at 06:54
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The fact that $I$ is non-countable is superfluous: you can reduce the problem to the countable case! – Dec 28 '13 at 09:47
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2@YACP Absolutely it is a duplicate; $\mathbb Z$-modules are free iff projective. – T.J. Gaffney Dec 28 '13 at 10:05