Extending properties of \(z\)-closed projection invariant submodules

Extending properties of \(z\)-closed projection invariant submodules

In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between...

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Date:2025
Main Authors: Yücel, Canan Celep, Ayvazoğlu, Yeşim
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2025
Subjects:
\(zp\)-submodule
\(z\)-closed submodule
\(PI\)-extending module
\(G\)-extending module
\(CS\)-module
16D50
16D70
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-2323
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-23232025-08-13T10:04:13Z Extending properties of \(z\)-closed projection invariant submodules Yücel, Canan Celep Ayvazoğlu, Yeşim \(zp\)-submodule, \(z\)-closed submodule, \(PI\)-extending module, \(G\)-extending module, \(CS\)-module 16D50, 16D70 In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between the other extending properties. Our focus is the behavior of the \(ZPG\) modules with respect to direct sums and direct summands. We obtain the property is closed under right essential overring and rational hull. Lugansk National Taras Shevchenko University 2025-08-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323 10.12958/adm2323 Algebra and Discrete Mathematics; Vol 39, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1248 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1302 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2323/1303 Copyright (c) 2025 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2025-08-13T10:04:13Z
collection OJS
language English
topic \(zp\)-submodule
\(z\)-closed submodule
\(PI\)-extending module
\(G\)-extending module
\(CS\)-module
16D50
16D70
spellingShingle \(zp\)-submodule
\(z\)-closed submodule
\(PI\)-extending module
\(G\)-extending module
\(CS\)-module
16D50
16D70
Yücel, Canan Celep
Ayvazoğlu, Yeşim
Extending properties of \(z\)-closed projection invariant submodules
topic_facet \(zp\)-submodule
\(z\)-closed submodule
\(PI\)-extending module
\(G\)-extending module
\(CS\)-module
16D50
16D70
format Article
author Yücel, Canan Celep
Ayvazoğlu, Yeşim
author_facet Yücel, Canan Celep
Ayvazoğlu, Yeşim
author_sort Yücel, Canan Celep
title Extending properties of \(z\)-closed projection invariant submodules
title_short Extending properties of \(z\)-closed projection invariant submodules
title_full Extending properties of \(z\)-closed projection invariant submodules
title_fullStr Extending properties of \(z\)-closed projection invariant submodules
title_full_unstemmed Extending properties of \(z\)-closed projection invariant submodules
title_sort extending properties of \(z\)-closed projection invariant submodules
description In this article, we define a module \(M\) to be \(ZPG\) if and only if for each \(zp\)-submodule \(X\) of \(M\) there exists a direct summand \(D\) such that \(X\cap D\) is essential in both \(X\) and \(D\). We investigate structural properties of \(ZPG\) modules and locate the implications between the other extending properties. Our focus is the behavior of the \(ZPG\) modules with respect to direct sums and direct summands. We obtain the property is closed under right essential overring and rational hull.
publisher Lugansk National Taras Shevchenko University
publishDate 2025
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2323
work_keys_str_mv AT yucelcanancelep extendingpropertiesofzclosedprojectioninvariantsubmodules
AT ayvazogluyesim extendingpropertiesofzclosedprojectioninvariantsubmodules
first_indexed 2025-09-17T09:26:09Z
last_indexed 2025-09-17T09:26:09Z
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