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Strongly 2T - Clean Rings | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 13, Volume 18, Issue 2, December 2024, Pages 101-104 PDF (334.67 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2024.150032.1128 | ||
| Authors | ||
| Zeina M Hamady* 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 a in a ring R is referred to be strongly 2T-clean (2 – STC element for short), a = Ω-Λ+u, where Ω,Λ are idempotent elements and u is a unit elements of order three. A ring R is considered to be 2 - STC ring if every member of R are 2 - STC ring. This paper presents the idea of an strongly 2T-clean ring and lists some of its fundamental characteristics. Further more we consider 2 - STC ring with 3 is nilpotent, we demonstrate that this ring is equivalent to strongly 2- nil clean ring and the Jacobson radical and the right singular ideal of such ring with 3 is nilpotent is a nil ideal. Finally we exhibit that if R is an 2 - STC ring and if 2 is nilpotent, then a^4-a is nilpotent for every a in R. We domonstrale that if R is 2 - STC ring, then a∈R such that a = Ω-h+u, Ω is idempotent, h is a unit of order two and u is a unit of order three. | ||
| Keywords | ||
| Idempotent; nilpotent; unit; strongly 2- nil clean; good ring | ||
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