Amply (weakly) Goldie-Rad-supplemented modules
Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supp...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543155791331328 |
|---|---|
| author | Takıl Mutlu, Figen |
| author_facet | Takıl Mutlu, Figen |
| author_sort | Takıl Mutlu, Figen |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-11-15T13:03:03Z |
| description | Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supplemented if every submodule of \(M\) has ample (weak) Goldie-Rad-supplements in \(M\). In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if \(M\) is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then \(M\) is Artinian. |
| first_indexed | 2026-02-08T07:58:44Z |
| format | Article |
| id | admjournalluguniveduua-article-59 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:44Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-592016-11-15T13:03:03Z Amply (weakly) Goldie-Rad-supplemented modules Takıl Mutlu, Figen Supplement submodule, Goldie-Rad-Supplement submodule, amply Goldie-Rad-Supplemented module 16D10, 16D40, 16D70 Let \(R\) be a ring and \(M\) be a right \(R\)-module. We say a submodule \(S\) of \(M\) is a \textit{(weak) Goldie-Rad-supplement} of a submodule \(N\) in \(M\), if \(M=N+S\), \((N\cap S \leq Rad(M))\) \(N\cap S\leq Rad(S)\) and \(N\beta^{**} S\), and \(M\) is called amply (weakly) Goldie-Rad-supplemented if every submodule of \(M\) has ample (weak) Goldie-Rad-supplements in \(M\). In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if \(M\) is amply (weakly) Goldie-Rad-supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then \(M\) is Artinian. Lugansk National Taras Shevchenko University This study was supported by Anadolu University Scientific Research Projects Commission under the grant no:1505F225. 2016-11-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 Algebra and Discrete Mathematics; Vol 22, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/59/129 Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 Takıl Mutlu, Figen Amply (weakly) Goldie-Rad-supplemented modules |
| title | Amply (weakly) Goldie-Rad-supplemented modules |
| title_full | Amply (weakly) Goldie-Rad-supplemented modules |
| title_fullStr | Amply (weakly) Goldie-Rad-supplemented modules |
| title_full_unstemmed | Amply (weakly) Goldie-Rad-supplemented modules |
| title_short | Amply (weakly) Goldie-Rad-supplemented modules |
| title_sort | amply (weakly) goldie-rad-supplemented modules |
| topic | Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 |
| topic_facet | Supplement submodule Goldie-Rad-Supplement submodule amply Goldie-Rad-Supplemented module 16D10 16D40 16D70 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/59 |
| work_keys_str_mv | AT takılmutlufigen amplyweaklygoldieradsupplementedmodules |