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On Strongly SITN Rings | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 15, Volume 18, Issue 2, December 2024, Pages 111-114 PDF (354.18 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2024.150182.1132 | ||
| Authors | ||
| Rafal R Dhanoon* 1; Nazar H. Shuker2 | ||
| 1Department of Mathematics college of computer sciences and Mathematics University of Mosul, | ||
| 2Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| nilpotent; idempotent; tripotent; strongly nil clean | ||
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