$Modules whose maximal submodules have $\tau$-supplements$

Modules whose maximal submodules have $\tau$-supplements

Let $R$ be a ring and $\tau$ be a preradical for the category of left $R$-modules. In this paper, we study on modules whose maximal submodules have $\tau$-supplements. We give some characterizations of these modules in terms their certain submodules, so called $\tau$-local submodules. For...

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Дата:	2018
Автор:	Buyukasık, Engin
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	preradical $\tau$-supplement $\tau$-local 16D10 16N80
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-646
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-6462018-04-04T09:17:05Z Modules whose maximal submodules have $\tau$-supplements Buyukasık, Engin preradical, $\tau$-supplement, $\tau$-local 16D10, 16N80 Let $R$ be a ring and $\tau$ be a preradical for the category of left $R$-modules. In this paper, we study on modules whose maximal submodules have $\tau$-supplements. We give some characterizations of these modules in terms their certain submodules, so called $\tau$-local submodules. For some certain preradicals $\tau$, i.e. $\tau=\delta$ and idempotent $\tau$, we prove that every maximal submodule of $M$ has a $\tau$-supplement if and only if every cofinite submodule of $M$ has a $\tau$-supplement. For a radical $\tau$ on $\operatorname{R-Mod}$, we prove that, for every $R$-module every submodule is a $\tau$-supplement if and only if $R/\tau(R)$ is semisimple and $\tau$ is hereditary. 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/646 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646/180 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T09:17:05Z
collection	OJS
language	English
topic	preradical $\tau$-supplement $\tau$-local 16D10 16N80
spellingShingle	preradical $\tau$-supplement $\tau$-local 16D10 16N80 Buyukasık, Engin Modules whose maximal submodules have $\tau$-supplements
topic_facet	preradical $\tau$-supplement $\tau$-local 16D10 16N80
format	Article
author	Buyukasık, Engin
author_facet	Buyukasık, Engin
author_sort	Buyukasık, Engin
title	Modules whose maximal submodules have $\tau$-supplements
title_short	Modules whose maximal submodules have $\tau$-supplements
title_full	Modules whose maximal submodules have $\tau$-supplements
title_fullStr	Modules whose maximal submodules have $\tau$-supplements
title_full_unstemmed	Modules whose maximal submodules have $\tau$-supplements
title_sort	modules whose maximal submodules have $\tau$-supplements
description	Let $R$ be a ring and $\tau$ be a preradical for the category of left $R$-modules. In this paper, we study on modules whose maximal submodules have $\tau$-supplements. We give some characterizations of these modules in terms their certain submodules, so called $\tau$-local submodules. For some certain preradicals $\tau$, i.e. $\tau=\delta$ and idempotent $\tau$, we prove that every maximal submodule of $M$ has a $\tau$-supplement if and only if every cofinite submodule of $M$ has a $\tau$-supplement. For a radical $\tau$ on $\operatorname{R-Mod}$, we prove that, for every $R$-module every submodule is a $\tau$-supplement if and only if $R/\tau(R)$ is semisimple and $\tau$ is hereditary.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646
work_keys_str_mv	AT buyukasıkengin moduleswhosemaximalsubmoduleshavetausupplements
first_indexed	2025-07-17T10:35:35Z
last_indexed	2025-07-17T10:35:35Z
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Modules whose maximal submodules have \(\tau\)-supplements

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