A morphic ring of neat range one
We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat ele...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/57 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | We show that a commutative ring \(R\) has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring \(R\) has a neat range one if and only if for any elements \(a, b \in R\) such that \(aR=bR\) there exist neat elements \(s, t \in R\) such that \(bs=c\), \(ct=b\). Examples of morphic rings of neat range one are given. |
|---|