On Strongly SITN Rings
An element is considered as a strongly SITN, if it is the sum of idempotent, tripotent and a nilpotent, that commute with one another. A ring R is referred to be SITN ring if each member of R is a strongly SITN. In this paper additional properties of a strongly SITN – ring are give. We pro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mosul University
2024-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.uomosul.edu.iq/article_185899_17afdd0e9b4127aa061d25b277c57dc1.pdf |
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| Summary: | An element is considered as a strongly SITN, if it is the sum of idempotent, tripotent and a nilpotent, that commute with one another. A ring R is referred to be SITN ring if each member of R is a strongly SITN. In this paper additional properties of a strongly SITN – ring are give. We prove that if Ris a strongly SITN – ring, then a^5-5a^3+4a is a nilpotent for every a in R, we also give a necessary and sufficient condition for a strongly SITN ring to be a strongly nil clean ring. Among other result, we show that the Jacobson radical of a strongly SITN is a nil ideal. Finally, we consider a special strongly SITN-ring. |
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| ISSN: | 1815-4816 2311-7990 |