Strongly nil *-clean rings

Abstract

A * -ring R is called strongly nil * -clean if every element of R is the sum of a projection and a nilpotent element that commute with each other. In this paper we investigate some properties of strongly nil * -rings and prove that R is a strongly nil * -clean ring if and only if every idempotent in R is a projection, R is periodic, and R/J(R) is Boolean. We also prove that a * -ring R is commutative, strongly nil * -clean and every primary ideal is maximal if and only if every element of R is a projection.