• ON A SUBCLASS OF SEMIPOTENT RINGS

Abstract

A ring R is said to be clean if every element of R is sum of an idempotent and a unit in R. We define a ring R to be a root clean ring if every element of R can be written as a sum of a unit and a square root of 1. In this paper we study root clean rings and its relationship with clean rings and semiboolean rings. Also we obtain some interesting results on semipotent rings.

2010 Mathematics subject classification: 16E50, 16U99.

Key Words: exchange ring, clean ring, strongly clean ring.