Semi Nilpotent Elements
In this paper we study semi nilpotent elements in rings. It is shown that every element of Z nwhere n is square free is a trivial semi nilpotent. It is proved that every nontrivial nilpotent element is a nontrivial semi nilpotent. Conditions are given under which every element of the group ring ZnG...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Tishk International University
2017-12-01
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| Series: | Eurasian Journal of Science and Engineering |
| Subjects: | |
| Online Access: | http://eajse.org/wp-content/uploads/2015/12/Semi-Nilpotent-Elements.pdf |
| Summary: | In this paper we study semi nilpotent elements in rings. It is shown that every element of Z nwhere n is square free is a trivial semi nilpotent. It is proved that every nontrivial nilpotent element is a nontrivial semi nilpotent. Conditions are given under which every element of the group ring ZnG is semi nilpotent. It is shown that if p is prime and p divides the order of G, then ZpG has nontrivial semi nilpotent. Also it is proved that if G is a cyclic group of order qn, then every element of ZpG, p is prime, is semi nilpotent. |
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| ISSN: | 2414-5629 2414-5602 |