الملخص

In this paper, we present the idea of a strongly invo. T-clean rings, which we define as rings with every a in R having the formula a = t + v, where t is a tripotent and v is an order two unit that commute. Such rings fundamental properties are given, and its connection with other related rings is obtained. we consider a strongly Tri nil clean ring as a ring R with every element a in R can be expressed as a sum of a tripotent and a nilpotent that commute, and we explore the Jacobson radical over strongly Invo. T-clean ring.