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The Strongly Tri-nil Clean Rings | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 9, Volume 19, Issue 1, June 2025, Pages 80-83 PDF (398.25 K) | ||
| Document Type: Review Paper | ||
| DOI: 10.33899/csmj.2025.156371.1164 | ||
| Authors | ||
| Rana Mahammed Shafik* 1; Nazar H. Shuker2 | ||
| 1Department Mathematics, Computer Science and Mathematics, Mosul, Iraq | ||
| 2Mathematics dept, Computer Science and Mathematics, Mosul, Iraq | ||
| Abstract | ||
| This study explores the structure and properties of strongly Tri-nil clean rings. A ring is defined as strongly Tri-nil clean if every member in a ring can be expressed as the sum of a tripotent element and a nilpotent member, where these components commute. We provide the right singular ideal of a ring which is a nil ideal. We examine a ring with each element σ in R,σ^2 is zhou. we also found in these rings the char(R)=48, and every unit of order 4, Finally, we provide if R is a Tri-nil clean ring with 3∈N(R) if and only if every member of R is a sum of three tripotent and nilpotent that commute. | ||
| Keywords | ||
| tripotent; nilpotent; unit; Jacobson radical; good ring | ||
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