Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4585263 | Journal of Algebra | 2013 | 6 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pedro A. Guil Asensio, Ashish K. Srivastava,