- All Journals
- Al-Qadisiyah University
- Basrah University
- Kirkuk University
- Mosul University
- The Iraqi Borad for Medical Specialization
- University of Anbar
- University of Technology
- Al Mustafa University
- Al-Zahraa University for Women
- Alnoor University
- Kunooz University
- Misan University
- Ninevah University
- Tikrit University
- University of Al-Hamdaniya
- University of Kerbala
The Strongly Nil-Clean Rings Of Order Two Units | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 10, Volume 18, Issue 2, December 2024, Pages 82-86 PDF (378.17 K) | ||
| Document Type: Review Paper | ||
| DOI: 10.33899/csmj.2024.149121.1119 | ||
| Authors | ||
| Samira Beno Toma* 1; Nazar H. Shuker2 | ||
| 1Department of Mathematics College of Computer Sciences and Mathematics, Mosul University | ||
| 2Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| If every element of a ring R is the sum of idempotent and nilpotent that commute, then the ring is said to be a strongly nil-clean. Further features of a strongly nil-clean ring are given in this paper. Furthermore, we present and investigate a special class of strongly nil-clean rings with order two units. Additionally, we examine a ring with each element a in R, a2 and a4 is a strongly nil-clean with order two and order four units. Among other results, we prove that: If R is a strongly nil-clean ring of order two units, then for all a in R, existing b in R, such that a.b=Ψ,a-b-1=u and u2=1, and the converse of this result is true if 2 is nilpotent. | ||
| Keywords | ||
| strongly nil-clean; Idempotent element; Nilpotent element | ||
|
Statistics Article View: 183 PDF Download: 60 |
||