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 |
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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 |
| _version_ | 1797761233578885120 |
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| author | Kurdistan M. Ali Parween A. Hummadi |
| author_facet | Kurdistan M. Ali Parween A. Hummadi |
| author_sort | Kurdistan M. Ali |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T19:10:59Z |
| format | Article |
| id | doaj.art-4f29a7c222ac47b1afcfa24efe2f4d94 |
| institution | Directory Open Access Journal |
| issn | 2414-5629 2414-5602 |
| language | English |
| last_indexed | 2024-03-12T19:10:59Z |
| publishDate | 2017-12-01 |
| publisher | Tishk International University |
| record_format | Article |
| series | Eurasian Journal of Science and Engineering |
| spelling | doaj.art-4f29a7c222ac47b1afcfa24efe2f4d942023-08-02T05:55:31ZengTishk International UniversityEurasian Journal of Science and Engineering2414-56292414-56022017-12-013224124610.23918/eajse.v3i2p241Semi Nilpotent ElementsKurdistan M. Ali Parween A. HummadiIn 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.http://eajse.org/wp-content/uploads/2015/12/Semi-Nilpotent-Elements.pdfNilpotentSemi Nilpotent |
| spellingShingle | Kurdistan M. Ali Parween A. Hummadi Semi Nilpotent Elements Eurasian Journal of Science and Engineering Nilpotent Semi Nilpotent |
| title | Semi Nilpotent Elements |
| title_full | Semi Nilpotent Elements |
| title_fullStr | Semi Nilpotent Elements |
| title_full_unstemmed | Semi Nilpotent Elements |
| title_short | Semi Nilpotent Elements |
| title_sort | semi nilpotent elements |
| topic | Nilpotent Semi Nilpotent |
| url | http://eajse.org/wp-content/uploads/2015/12/Semi-Nilpotent-Elements.pdf |
| work_keys_str_mv | AT kurdistanmali seminilpotentelements AT parweenahummadi seminilpotentelements |