IJPAM: Volume 32, No. 1 (2006)

ON LEFT NEGATIVELY ORDERED RPP SEMIGROUPS

Xiaojiang Guo$^1$, Wei Chen$^2$, K.P. Shum$^3$
$^1$Department of Mathematics
Jiangxi Normal University
Nanchang, Jiangxi, 330022, P.R. CHINA
e-mail: xjguo1967@sohu.com
$^2$Department of Mathematics
Northwest University
Xi'an, Shanxi, P.R. CHINA
$^3$Department of Mathematics
Faculty of Science
The Chinese University of Hong Kong
Shatin, N.T., HONG KONG, P.R. CHINA (SAR)
e-mail: kpshum@math.cuhk.edu.hk


Abstract.A semigroup $S$ equipped with a partial order $\lq\lq \leq''$ is called a left negatively ordered semigroup if $ab\leq a,$ for all $a,b\in S$. In this paper, we study the rpp semigroups equipped with the left negative Lawson partial order $\lq\lq \leq_\ell''$. In particular, we establish a structure theorem for the left negatively ordered rpp semigroups on which the Green relation $\mathcal{L}$ is a congruence. Some results recently obtained by Guo and Shum on rpp semigroups equipped with the Lawson negative partial order $\lq\lq \leq_\ell''$ are extended and generalized.

Received: September 27, 2006

AMS Subject Classification: 20M10

Key Words and Phrases: Rpp semigroup, GV-semigroup, left regular band, semilattice

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 1