Essentially iso-retractable modules and rings

A. K. Chaturvedi; S. Kumar; S. Prakash; N. Kumar

doi:10.15330/cmp.14.1.76-85

Essentially iso-retractable modules and rings

A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar

University of Allahabad

Research output: Contribution to journal › Article › peer-review

Abstract

A.K. Chaturvedi et al. (2021) call a module M essentially iso-retractable if for every essential submodule N of M there exists an isomorphism f: M → N. We characterize essentially iso-retractable modules, co-semisimple modules (V-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.

Original language	English
Pages (from-to)	76-85
Number of pages	10
Journal	Carpathian Mathematical Publications
Volume	14
Issue number	1
DOIs	https://doi.org/10.15330/cmp.14.1.76-85
State	Published - 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Chaturvedi A.K., Kumar S., Prakash S., Kumar N., 2022.

Keywords

essentially compressible module
essentially iso-retractable module
iso-retractable module
retractable module

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10.15330/cmp.14.1.76-85

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PY - 2022

Y1 - 2022

N2 - A.K. Chaturvedi et al. (2021) call a module M essentially iso-retractable if for every essential submodule N of M there exists an isomorphism f: M → N. We characterize essentially iso-retractable modules, co-semisimple modules (V-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.

AB - A.K. Chaturvedi et al. (2021) call a module M essentially iso-retractable if for every essential submodule N of M there exists an isomorphism f: M → N. We characterize essentially iso-retractable modules, co-semisimple modules (V-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.

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KW - essentially iso-retractable module

KW - iso-retractable module

KW - retractable module

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Essentially iso-retractable modules and rings

Abstract

Bibliographical note

Keywords

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