Strongly 2-Nil Clean Rings with Units of Order Two


  • Renas M.Salim University of Zakho
  • Nazar H. Shuker Department of Math. College of Computer Science and Math. Mosul University



Clean, Nil clean, Strongly 2-nil clean, Tripotent


A ring R is considered a strongly 2-nil clean ring, or (strongly 2-NC ring for short), if each element in R can be expressed as the sum of a nilpotent and two idempotents that commute with each other. In this paper, further properties of strongly 2-NC rings are given. Furthermore, we introduce and explore a special type of strongly 2-NC ring where every unit is of order 2, which we refer to as a strongly 2-NC rings with U(R) = 2. It was proved that the Jacobson radical over a strongly 2-NC ring is a nil ideal, here, we demonstrated that the Jacobson radical over strongly 2-NC ring with U(R) = 2 is a nil ideal of characteristic 4. We compare this ring with other rings, since every SNC ring is strongly 2-NC, but not every unit of order 2, and if R is a strongly 2-NC with U(R) = 2, then R need not be SNC ring. In order to get N il(R) = 0, we added one more condition involving this ring.




How to Cite

M.Salim, R., & Shuker, N. (2023). Strongly 2-Nil Clean Rings with Units of Order Two. European Journal of Pure and Applied Mathematics, 16(3), 1675–1684.



Nonlinear Analysis