Recall that Schanuel’s lemma asserts that if are short exact sequences and is projective, then . Show this fails if the are only assumed to be flat.

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# Schanuel’s lemma fails for flats

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Recall that Schanuel’s lemma asserts that if are short exact sequences and is projective, then . Show this fails if the are only assumed to be flat.

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*Hint* As in the previous post, the integers work. In fact, this fails even if only one of the is flat.

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