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Aug 20, 2021 at 20:40 comment added Nik Weaver Yeah, I guess the first places I look for Hilbert module counterexamples are when $E$ is commutative, or when $E$ is a module over itself (or, in this case, both).
Aug 20, 2021 at 20:35 vote accept Andromeda
Aug 20, 2021 at 20:35 comment added Andromeda Thanks! Nice example. I should keep this in mind.
Aug 20, 2021 at 20:31 history answered Nik Weaver CC BY-SA 4.0