IJPAM: Volume 53, No. 4 (2009)

GENERALIZED QUASI HAMILTONIAN SEMIGROUPS

K.P. Shum$^1$, Liang Zhang$^2$
$^1$Department of Mathematics
The University of Hong Kong
Pokfulam Road, HONG KONG (SAR), P.R. CHINA
e-mail: [email protected] hku.hk
$^2$Department of Applied Mathematics
Tongji University
Shanghai, 200092, P.R. CHINA


Abstract.Super Hamiltonian semigroups were considered by K.P. Shum and X.M. Ren in 2004. In their previous paper, it was proved that a semigroup is a super Hamiltonian if and only if it is expressible as a strong semilattice of quasi-groups. However, the above result does not hold in general. In this paper, we consider the quasi periodic groups and accordingly, we give a characterization theorem for the generalized quasi Hamiltonian semigroups. Some subclasses of generalized quasi Hamiltonian semigroups are discussed and some results obtained by Cherubini and Varisco on quasi Hamiltonian semigroups are extended.

Received: May 11, 2006

AMS Subject Classification: 20M10

Key Words and Phrases: generalized Hamiltonian semigroups, super Hamiltonian semigroups, strong semilattice of semigroups

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 4