On Semiabelian π-Regular Rings
A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a sem...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/63171 |
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| _version_ | 1850165156102799360 |
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| author | Weixing Chen |
| author_facet | Weixing Chen |
| author_sort | Weixing Chen |
| collection | DOAJ |
| description | A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a semiabelian ring R is π-regular if and only if N(R) is an ideal of R and R/N(R) is regular, which extends the fundamental result of Badawi (1997). Moreover, several related results and examples are
given. |
| format | Article |
| id | doaj-art-ebd78c4ce05043fb8b7444b5aec5e440 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ebd78c4ce05043fb8b7444b5aec5e4402025-08-20T02:21:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6317163171On Semiabelian π-Regular RingsWeixing Chen0School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, ChinaA ring R is defined to be semiabelian if every idempotent of R is either right semicentral or left semicentral. It is proved that the set N(R) of nilpotent elements in a π-regular ring R is an ideal of R if and only if R/J(R) is abelian, where J(R) is the Jacobson radical of R. It follows that a semiabelian ring R is π-regular if and only if N(R) is an ideal of R and R/N(R) is regular, which extends the fundamental result of Badawi (1997). Moreover, several related results and examples are given.http://dx.doi.org/10.1155/2007/63171 |
| spellingShingle | Weixing Chen On Semiabelian π-Regular Rings International Journal of Mathematics and Mathematical Sciences |
| title | On Semiabelian π-Regular Rings |
| title_full | On Semiabelian π-Regular Rings |
| title_fullStr | On Semiabelian π-Regular Rings |
| title_full_unstemmed | On Semiabelian π-Regular Rings |
| title_short | On Semiabelian π-Regular Rings |
| title_sort | on semiabelian π regular rings |
| url | http://dx.doi.org/10.1155/2007/63171 |
| work_keys_str_mv | AT weixingchen onsemiabelianpregularrings |