C2 Property of Column Finite Matrix Rings
A ring R is called a right C2 ring if any right ideal of R isomorphic to a direct summand of RR is also a direct summand. The ring R is called a right C3 ring if any sum of two independent summands of R is also a direct summand. It is well known that a right C2 ring must be a right C3 ring but the c...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/166322 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | C2 Property of Column Finite Matrix Rings / Liang Shen, Jianlong Chen // Український математичний журнал. — 2014. — Т. 66, № 12. — С. 1718–1722. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | A ring R is called a right C2 ring if any right ideal of R isomorphic to a direct summand of RR is also a direct summand. The ring R is called a right C3 ring if any sum of two independent summands of R is also a direct summand. It is well known that a right C2 ring must be a right C3 ring but the converse assertion is not true. The ring R is called J -regular if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. Let N be the set of natural numbers and let Λ be any infinite set. The following assertions are proved to be equivalent for a ring R:
(1) CFMFMN(R) is a right C2 ring;
(2) CFMFMΛ(R) is a right C2 ring;
(3) CFMFMN(R) is a right C3 ring;
(4) CFMFMΛ(R) is a right C3 ring;
(5) CFMFMN(R) is a J -regular ring and Mn(R) is a right C2 (or right C3) ring for all integers n≥1. |
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