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Iso-retractable modules and rings

A. K. Chaturvedi

A. K. Chaturvedi

Department of Mathematics, University of Allahabad, Allahabad-211002, India

E-mail Address: akc99@rediffmail.com

E-mail Address: akchaturvedi.math@gmail.com

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https://doi.org/10.1142/S179355711950013XCited by:5 (Source: Crossref)

Abstract

The modules which are isomorphic to their non-zero submodules are known as iso-retractable. We characterize simple modules in terms of iso-retractable modules. We provide several sufficient conditions for iso-retractable modules to be simple. We show that if the endomorphism ring of an iso-retractable module is von-Neumann regular then $M$ $M$ is a simple module. In general, iso-retractable modules need not be projective (injective) and vice versa. We investigate some properties of iso-retractable modules with projectivity as well as injectivity. Finally, we provide some open problems.

Communicated by V. S. Nguyen

Keywords:

AMSC: 16D50, 16D70, 16D80

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