IJPAM: Volume 1, No. 3 (2002)

ON RINGS WITH NEAR IDEMPOTENT ELEMENTS

A. Badawi$^1$, A.Y.M. Chin$^2$, H.V. Chen$^3$
$^1$Dept. of Mathematics
Birzeit University
P.O. Box 14, Birzeit, West Bank, Palestine via ISRAEL
e-mail: abring@birzeit.edu
$^{2,3}$Institute of Mathematical Sciences
Faculty of Science
University of Malaya, 50603 Kuala Lumpur, MALAYSIA
$^2$e-mail: acym@mnt.math.um.edu.my


Abstract.Let $R$ be an associative ring with unit. An element $e\in R$ is said to be a near idempotent if $e^n$ is an idempotent for some positive integer $n$. In this paper conditions on $R$ which are equivalent to the condition that $R$ has near idempotents as all its elements are obtained.

Received: January 31, 2002

AMS Subject Classification: 16E50, 16U99

Key Words and Phrases: idempotent, strongly $\pi$-regular, strongly regular, $(s,2)$-ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 3