The strongly Tri-nil clean rings

This study explores the structure and properties of strongly Tri-nil clean rings. A ring is defined as strongly Tri-nil clean if every member in a ring can be expressed as the sum of a tripotent element and a nilpotent member, where these components commute. We provide the right singular ideal of a ring which is a nil ideal. We examine a ring with each element in R,^2 is zhou. we also found in these rings the char(R)=48, and every unit of order 4, Finally, we provide if R is a Tri-nil clean ring with 3N(R) if and only if every member of R is a sum of three tripotent and nilpotent that commute.