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arXiv · 1304.0056

Automorphism-invariant modules satisfy the exchange property

Pedro A Guil Asensio·Ashish K. Srivastava
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Abstract

Warfield proved that every injective module has the exchange property. This was generalized by Fuchs who showed that quasi-injective modules satisfy the exchange property. We extend this further and prove that a module invariant under automorphisms of its injective hull satisfies the exchange property. We also show that automorphism-invariant modules are clean and that directly-finite automorphism-invariant modules satisfy the internal cancellation and hence the cancellation property.

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Pedro A Guil Asensio, Ashish K. Srivastava. 2013-03-30. Automorphism-invariant modules satisfy the exchange property. https://arxiv.org/abs/1304.0056

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