JACOBSON MONOFORM MODULES

Document Type : Original Manuscript

Author

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

Abstract

In this paper, we introduce and study the concept of Jacobson monoform modules which
is a proper generalization of that of monoform modules. We present a characterization of semisimple
rings in terms of Jacobson monoform modules by proving that a ring $R$
is semisimple if and only if every $R$-module is Jacobson monoform. Moreover, we demonstrate that over a ring $R$, the properties monoform, Jacobson monoform, compressible, uniform and weakly co-Hopfian are all equivalent.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 379-390

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