The Strongly Nil-Clean Rings Of Order Two Units

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.