On periodic rings
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. Necessary and sufficient conditions are established for a ring to be a direct sum of a nil ring and a J-ring....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201001181 |
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| _version_ | 1832567297853620224 |
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| author | Xiankun Du Qi Yi |
| author_facet | Xiankun Du Qi Yi |
| author_sort | Xiankun Du |
| collection | DOAJ |
| description | It is proved that a ring is periodic if and only if, for any
elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. Necessary and sufficient conditions are
established for a ring to be a direct sum of a nil ring and a J-ring. |
| format | Article |
| id | doaj-art-357948578ecc43b688e0f0f0d5886c81 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-357948578ecc43b688e0f0f0d5886c812025-02-03T01:01:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125641742010.1155/S0161171201001181On periodic ringsXiankun Du0Qi Yi1Department of Mathematics, Jilin University, Changchun 130012, ChinaJilin Commercial College, Changchun 130062, ChinaIt is proved that a ring is periodic if and only if, for any elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. Necessary and sufficient conditions are established for a ring to be a direct sum of a nil ring and a J-ring.http://dx.doi.org/10.1155/S0161171201001181 |
| spellingShingle | Xiankun Du Qi Yi On periodic rings International Journal of Mathematics and Mathematical Sciences |
| title | On periodic rings |
| title_full | On periodic rings |
| title_fullStr | On periodic rings |
| title_full_unstemmed | On periodic rings |
| title_short | On periodic rings |
| title_sort | on periodic rings |
| url | http://dx.doi.org/10.1155/S0161171201001181 |
| work_keys_str_mv | AT xiankundu onperiodicrings AT qiyi onperiodicrings |