<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the past few decades, researchers have found that studying modules using endomorphisms is a powerful and useful tool. This has led to valuable works in this field. Recently, the study of (dual) Rickart modules has become an important approach as they are deeply connected to endomorphisms. Building on this work, the authors introduce a new perspective on (dual) Rickart modules using isomorphism. We also define virtually (dual) Rickart modules. It is shown that rings with all modules virtually Rickart are semisimple rings. The paper includes various examples to illustrate the concepts presented.</p>
</abstract>

In the past few decades, researchers have found that studying modules using endomorphisms is a powerful and useful tool. This has led to valuable works in this field. Recently, the study of (dual) Rickart modules has become an important approach as they are deeply connected to endomorphisms. Building on this work, the authors introduce a new perspective on (dual) Rickart modules using isomorphism. We also define virtually (dual) Rickart modules. It is shown that rings with all modules virtually Rickart are semisimple rings. The paper includes various examples to illustrate the concepts presented.

A new approach to (dual) Rickart modules via isomorphisms

Faculty of Mathematical Sciences University of Mazandaran

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A new approach to (dual) Rickart modules via isomorphisms"}

In the past few decades, researchers have found that studying modules using endomorphisms is a powerful and useful tool. This has led to valuable works in this...

A new approach to (dual) Rickart modules via isomorphisms

Published Online: Jul 10, 2024

Page range: 5 - 18

Received: May 08, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/auom-2024-0016

Keywords
annihilator, dual Rickart module, virtually Rickart module, virtually dual Rickart module, endomorphism ring

© 2024 S. Asgari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A new approach to (dual) Rickart modules via isomorphisms

Published Online: Jul 10, 2024

Page range: 5 - 18

Received: May 08, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/auom-2024-0016

Keywordsannihilator, dual Rickart module, virtually Rickart module, virtually dual Rickart module, endomorphism ring

© 2024 S. Asgari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
annihilator, dual Rickart module, virtually Rickart module, virtually dual Rickart module, endomorphism ring