A generalization of supplemented modules

Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a s...

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Date:	2018
Main Authors:	Inankil, Hatice, Halıcıoglu, Sait, Harmanci, Abdullah
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660
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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-660
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-6602018-04-04T09:21:34Z A generalization of supplemented modules Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah supplemented modules, \(\delta\)-supplemented modules, principally \(\delta\)-supplemented modules, semiperfect modules, \(\delta\)-semiperfect modules, principally \(\delta\)-semiperfect modules 16U80 Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a submodule \(A\) of \(M\) with \(M = mR + A\) and \((mR)\cap A\) \(\delta\)-small in \(A\). We prove that some results of \(\delta\)-supplemented modules can be extended to principally \(\delta\)-supplemented modules for this general settings. We supply some examples showing that there are principally \(\delta\)-supplemented modules but not \(\delta\)-supplemented. We also introduce principally \(\delta\)-semiperfect modules as a generalization of \(\delta\)-semiperfect modules and investigate their properties. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660 Algebra and Discrete Mathematics; Vol 11, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660/194 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T09:21:34Z
collection	OJS
language	English
topic	supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80
spellingShingle	supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80 Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah A generalization of supplemented modules
topic_facet	supplemented modules \(\delta\)-supplemented modules principally \(\delta\)-supplemented modules semiperfect modules \(\delta\)-semiperfect modules principally \(\delta\)-semiperfect modules 16U80
format	Article
author	Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah
author_facet	Inankil, Hatice Halıcıoglu, Sait Harmanci, Abdullah
author_sort	Inankil, Hatice
title	A generalization of supplemented modules
title_short	A generalization of supplemented modules
title_full	A generalization of supplemented modules
title_fullStr	A generalization of supplemented modules
title_full_unstemmed	A generalization of supplemented modules
title_sort	generalization of supplemented modules
description	Let \(R\) be an arbitrary ring with identity and \(M\) a right \(R\)-module. In this paper, we introduce a class of modules which is an analogous of \(\delta\)-supplemented modules defined by Kosan. The module \(M\) is called principally \(\delta\)-supplemented, for all \(m\in M\) there exists a submodule \(A\) of \(M\) with \(M = mR + A\) and \((mR)\cap A\) \(\delta\)-small in \(A\). We prove that some results of \(\delta\)-supplemented modules can be extended to principally \(\delta\)-supplemented modules for this general settings. We supply some examples showing that there are principally \(\delta\)-supplemented modules but not \(\delta\)-supplemented. We also introduce principally \(\delta\)-semiperfect modules as a generalization of \(\delta\)-semiperfect modules and investigate their properties.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/660
work_keys_str_mv	AT inankilhatice ageneralizationofsupplementedmodules AT halıcıoglusait ageneralizationofsupplementedmodules AT harmanciabdullah ageneralizationofsupplementedmodules AT inankilhatice generalizationofsupplementedmodules AT halıcıoglusait generalizationofsupplementedmodules AT harmanciabdullah generalizationofsupplementedmodules
first_indexed	2025-07-17T10:35:36Z
last_indexed	2025-07-17T10:35:36Z
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A generalization of supplemented modules

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