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Aug 21, 2019 at 8:52 comment added Jeremy Rickard Not a complete answer, but one necessary condition, which rules out many popular commutative rings, is that $k$ should have no finitely generated module $M$ with flat dimension equal to one.
Aug 20, 2019 at 20:27 history edited Mare CC BY-SA 4.0
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Aug 20, 2019 at 20:20 history edited Mare CC BY-SA 4.0
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Aug 20, 2019 at 14:54 history asked Mare CC BY-SA 4.0