IJPAM: Volume 29, No. 3 (2006)

THE LAWSON PARTIAL ORDER ON RPP SEMIGROUPS

Xiaojiang Guo$^1$, K.P. Shum$^2$
$^1$Department of Mathematics
Jiangxi Normal University
Nanchang, Jiangxi, 330027, P.R. CHINA
e-mail: xjguo@jxnu.edu.cn
$^2$Department of Mathematics
Faculty of Science
The Chinese University of Hong Kong
Shatin, New Territories, HONG KONG, P.R. CHINA
e-mail: kpshum@math.cuhk.edu.hk


Abstract.In this paper,we consider the natural partial order ``$\leq_\ell$'' on a semigroup. In particular, we will characterize the $rpp$ semigroup by using the Lawson partial order ``$\leq_\ell$'' which is (left; right) compatible with the semigroup multiplication. Our main result extends and generalizes a number of known results in the literature on the natural partial order on abundant semigroups and regular semigroups obtained by Nambooripad, Lawson, Blyth-Gomes and Guo-Luo, respectively.

Received: May 26, 2006

AMS Subject Classification: 20M10

Key Words and Phrases: Lawson partial order, $rpp$ semigroups, left regular bands, (locally) left $rpp$ semigroups, left quasi-normal bands

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 3