On a class of dual Rickart modules
UDC 512.5 Let $R$ be a ring and let $\Omega_R$ be the set of maximal right ideals of $R$. An $R$-module $M$ is called an sd-Rickart module if for every nonzero endomorphism $ f$ of $M$, $\Im f$ is a fully invariant direct summand of $M$. We obtain a characterization for an arbitrary direct sum of sd...
Збережено в:
| Дата: | 2020 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2020
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6021 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 512.5
Let $R$ be a ring and let $\Omega_R$ be the set of maximal right ideals of $R$. An $R$-module $M$ is called an sd-Rickart module if for every nonzero endomorphism $ f$ of $M$, $\Im f$ is a fully invariant direct summand of $M$. We obtain a characterization for an arbitrary direct sum of sd-Rickart modules to be sd-Rickart. We also obtain a decomposition of an sd-Rickart $R$-module $M$, provided $R$ is a commutative noetherian ring and $Ass(M) \cap \Omega_R$ is a finite set. In addition, we introduce and study ageneralization of sd-Rickart modules. |
|---|---|
| DOI: | 10.37863/umzh.v72i7.6021 |