Modules whose surjective endomorphisms have a $\gamma$-small kernels
نویسندگان
1 Department of Mathematics, Faculty of Sciences, University of Mohammed First Oujda, Morocco.
2 Department of Mathematics, Faculty of Sciences, University of Mohammed First, Oujda, Morocco.
doi
10.22034/as.2022.2677چکیده
In this paper, we introduce a proper generalization of that of Hopfian modules, called $\gamma$-Hopfian modules. A right $R$-module $M$ is said to be $\gamma$-Hopfian, if any surjective endomorphism of $M$ has a $\gamma$-small kernel. Some basic characterizations of $\gamma$-Hopfian modules are proved. We prove that a ring $R$ is semisimple cosingular if and only if every $R$-module is $\gamma$-Hopfian. Further, we prove that the $\gamma$-Hopfian property is preserved under Morita equivalences. Some other properties of $\gamma$-Hopfian modules are also obtained with examples.
