r-clean rings
Rings and Algebras
2011-05-04 v2
Abstract
An element of a ring R is called clean if it is the sum of an idempotent and a unit. A ring R is called clean if each of its element is clean. An element r \in R called regular if r = ryr for some y \in R. The ring R is regular if each of its element is regular. In this paper we define a ring is r-clean if each of its elements is the sum of a regular and an idempotent element. We give some relations between r-clean and clean rings. Finally we investigate some properties of r-clean rings.
Keywords
Cite
@article{arxiv.1104.2167,
title = {r-clean rings},
author = {Nahid Ashrafi and Ebrahim Nasibi},
journal= {arXiv preprint arXiv:1104.2167},
year = {2011}
}
Comments
7 pages