IJPAM: Volume 20, No. 4 (2005)

LEFT CENTRALIZERS OF SEMIPRIME RINGS

Mohammad S. Samman$^1$, Muhammad Anwar Chaudhry$^2$
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
P.O. Box 411, Dhahran, 31261, KINGDOM OF SAUDI ARABIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.In this paper we show that a mapping $T$ of a semiprime ring $R$ into itself is a centralizer if and only if it is a centralizing left centralizer. We also prove that if $T$ and $S$ are left centralizers of a semiprime ring $R$ satisfying $T(x)x + xS(x) \in Z(R)$ (the center of $R$) for all $x\in R$, then both $T$ and $S$ are centralizers.

Received: March 15, 2005

AMS Subject Classification: 16A12, 16A68, 16A72, 16N60

Key Words and Phrases: semiprime ring, left (right) centralizer, centralizer, commuting mapping, centralizing mapping, extended centroid

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 4