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 ∈ R such that aR=bR there exist neat elements s,t∈R such th...
Збережено в:
| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155168 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A morphic ring of neat range one / O. Pihura, B. Zabavsky // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 325-329. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| 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 ∈ R such that aR=bR there exist neat elements s,t∈R such that bs=c, ct=b. Examples of morphic rings of neat range one are given. |
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