Strongly nil *-clean rings

Year 2017, , 155 - 164, 11.01.2017

Abdullah Harmanci , Huanyin Chen , A. Cigdem Ozcan

https://doi.org/10.13069/jacodesmath.284954

Cited By: 1

Abstract

A $*$-ring $R$ is called {\em 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.

Keywords

Rings with involution, Boolean ring, Strongly nil *-clean ring, *-Boolean ring

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