IJPAM: Volume 55, No. 3 (2009)

ON PRIMARY IDEALS AND RADICALS OF
ORDERED SEMIGROUPS

Qing-Shun Zhu
Department of Applied Mathematics and Physics
Institute of Sciences
Information Engineering University
No. 93, Science Road, Zhengzhou, 450001, P.R. CHINA
e-mail: qingshunzhu@yahoo.com.cn


Abstract.In this paper, we introduce the concept of the primary ideal of $po-$semigroups and give some characterizations of primary ideal of $po-$semigroups. In particular, for commutative $po-$semigroups, we also prove that every proper ideal can be expressed as an intersection of finite primary ideals.

Received: July 2, 2008

AMS Subject Classification: 20M10, 06F05

Key Words and Phrases: $po$-semigroup, ideal, prime ideal, primary ideal, radical of $po$-semigroup

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3