On Strongly SITN Rings

Abstract

An element is considered as a strongly SITN, if it is the sum of idempotent, tripotent and a nilpotent, that commute with one another. A ring R is referred to be SITN ring if each member of R is a strongly SITN. In this paper additional properties of a strongly SITN – ring are give. We prove that if Ris a strongly SITN – ring, then a^5-5a^3+4a is a nilpotent for every a in R, we also give a necessary and sufficient condition for a strongly SITN ring to be a strongly nil clean ring. Among other result, we show that the Jacobson radical of a strongly SITN is a nil ideal. Finally, we consider a special strongly SITN-ring.

Keywords

• nilpotent
• idempotent
• tripotent
• strongly nil clean