Generalizations of $\oplus$-supplemented modules
We introduce $\oplus$-radical supplemented modules and strongly $\oplus$-radical supplemented modules (briefly, $srs^{\oplus}$-modules) as proper generalizations of $\oplus$-supplemented modules. We prove that (1) a semilocal ring $R$ is left perfect if and only if every left $R$-module is an $\opl...
Збережено в:
| Дата: | 2013 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2013
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2439 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We introduce $\oplus$-radical supplemented modules and strongly $\oplus$-radical supplemented modules (briefly, $srs^{\oplus}$-modules) as proper generalizations of $\oplus$-supplemented modules.
We prove that (1) a semilocal ring $R$ is left perfect if and only if every left $R$-module is an $\oplus$-radical supplemented module;
(2) a commutative ring $R$ is an Artinian principal ideal ring if and only if every left $R$-module is a $srs^{\oplus}$-module;
(3) over a local Dedekind domain, every $\oplus$-radical supplemented module is a $srs^{\oplus}$-module. Moreover, we completely determine the structure of these modules over local Dedekind domains. |
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