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Paper   IPM / M / 741
School of Mathematics
  Title:   Modules whose injective endomorphisms are essential
1.  A. Haghany
2.  M. R. Vedadi
  Status:   Published
  Journal: J. Algebra
  No.:  2
  Vol.:  243
  Year:  2001
  Pages:   765-779
  Supported by:  IPM
An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential. The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and the class of Dedekind finite modules. Several equivalent conditions are given for a module to be weakly co-Hopfian. Being co-Hopfian, weakly co-Hopfian or Dedekind finite are all equivalent conditions on quasi-injective modules. Some other properties of weakly co-Hopfian modules are also obtained.

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