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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Hindawi Limited
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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doaj-ebd78c4ce05043fb8b7444b5aec5e4402020-11-24T23:02:42ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Weixing Chen |
| spellingShingle |
Weixing Chen On Semiabelian π-Regular Rings International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Weixing Chen |
| author_sort |
Weixing Chen |
| title |
On Semiabelian π-Regular Rings |
| title_short |
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_sort |
on semiabelian π-regular rings |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2007-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2007/63171 |
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AT weixingchen onsemiabelianpregularrings |
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