Article ID Journal Published Year Pages File Type
4585263 Journal of Algebra 2013 6 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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