“School of Mathematics”
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| Paper IPM / M / 741 | ||||||||||||||||||||||||
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| Abstract: | ||||||||||||||||||||||||
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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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