Modules which have a rad-supplement that is a direct summand in every extension

Modules which have a rad-supplement that is a direct summand in every extension

In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module \(M\) is \(\operatorname{Rad}\)-supplementing if and only if \(M\) has the property (SRE). Moreover, we show tha...

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Збережено в:
Бібліографічні деталі
Дата:2018
Автори: Türkmen, Burcu Nişancı, Türkmen, Ergül
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2018
Теми:
\(\operatorname{Rad}\)-supplement
module with the properties (RE) and (SRE)
artinian serial ring
16D10
16D50
16N80
Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/159
Теги: Додати тег
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Назва журналу:Algebra and Discrete Mathematics

Репозитарії

Algebra and Discrete Mathematics
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record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-1592018-05-17T07:54:05Z Modules which have a rad-supplement that is a direct summand in every extension Türkmen, Burcu Nişancı Türkmen, Ergül \(\operatorname{Rad}\)-supplement, module with the properties (RE) and (SRE), artinian serial ring 16D10, 16D50, 16N80 In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module \(M\) is \(\operatorname{Rad}\)-supplementing if and only if \(M\) has the property (SRE). Moreover, we show that a ring \(R\) is a left V-ring if and only if every left \(R\)-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE). Lugansk National Taras Shevchenko University 2018-04-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/159 Algebra and Discrete Mathematics; Vol 25, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/159/pdf Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-05-17T07:54:05Z
collection OJS
language English
topic \(\operatorname{Rad}\)-supplement
module with the properties (RE) and (SRE)
artinian serial ring
16D10
16D50
16N80
spellingShingle \(\operatorname{Rad}\)-supplement
module with the properties (RE) and (SRE)
artinian serial ring
16D10
16D50
16N80
Türkmen, Burcu Nişancı
Türkmen, Ergül
Modules which have a rad-supplement that is a direct summand in every extension
topic_facet \(\operatorname{Rad}\)-supplement
module with the properties (RE) and (SRE)
artinian serial ring
16D10
16D50
16N80
format Article
author Türkmen, Burcu Nişancı
Türkmen, Ergül
author_facet Türkmen, Burcu Nişancı
Türkmen, Ergül
author_sort Türkmen, Burcu Nişancı
title Modules which have a rad-supplement that is a direct summand in every extension
title_short Modules which have a rad-supplement that is a direct summand in every extension
title_full Modules which have a rad-supplement that is a direct summand in every extension
title_fullStr Modules which have a rad-supplement that is a direct summand in every extension
title_full_unstemmed Modules which have a rad-supplement that is a direct summand in every extension
title_sort modules which have a rad-supplement that is a direct summand in every extension
description In this paper, we introduce the concept of modules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module \(M\) is \(\operatorname{Rad}\)-supplementing if and only if \(M\) has the property (SRE). Moreover, we show that a ring \(R\) is a left V-ring if and only if every left \(R\)-module with the property (RE) is injective. Finally, we characterize the rings whose modules have the properties (RE) and (SRE).
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/159
work_keys_str_mv AT turkmenburcunisancı moduleswhichhavearadsupplementthatisadirectsummandineveryextension
AT turkmenergul moduleswhichhavearadsupplementthatisadirectsummandineveryextension
first_indexed 2025-07-17T10:36:12Z
last_indexed 2025-07-17T10:36:12Z
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