TY - JOUR
AU - M.Salim, Renas
AU - Shuker, Nazar
PY - 2023/07/30
Y2 - 2023/12/05
TI - Strongly 2-Nil Clean Rings with Units of Order Two
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 3
SE -
DO - 10.29020/nybg.ejpam.v16i3.4797
UR - https://ejpam.com/index.php/ejpam/article/view/4797
SP - 1675-1684
AB - <p>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.</p>
ER -