Hopfcity and Jacobson small submodules

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences, University of Mohammed First Oujda, Morocco.

Abstract

The study of modules by properties of their endomorphisms has long been of interest. In this paper, we introduce the notion of jacobson weakly Hopfian modules. It is shown that over a ring $R$, every projective (free) $R$-module is jacobson weakly Hopfian if and only if $R$ has no nonzero semisimple projective $R$-module. Let $L$ be a module such that $L$ satisfies ascending chain conditions on jacobson-small submodules. Then it is shown that $L$ is jacobson weakly Hopfian. Some basic characterizations of projective jacobson weakly Hopfian modules are proved.

Keywords

References

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Algebraic Structures and Their Applications
Volume 10, Issue 2
August 2023
Pages 31-40

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