ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS

- Journal title : Communications of the Korean Mathematical Society
- Volume 23, Issue 1, 2008, pp.19-27
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2008.23.1.019

Title & Authors

ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS

Siripitukdet, Manoj; Iampan, Aiyared;

Siripitukdet, Manoj; Iampan, Aiyared;

Abstract

The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) -semigroups. In 1981, Sen [8] has introduced the concept of the -semigroups. We can see that any semigroup can be considered as a -semigroup. The concept of ordered ideal extensions in ordered -semigroups was introduced in 2007 by Siripitukdet and Iampan [12]. Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered -semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered -semigroups.

Keywords

(ordered) semigroup;(ordered) -semigroup;(ordered) ideal;ordered ideal extension;(ordered) prime ideal;(ordered) semiprime ideal;ordered n-prime ideal and ordered n-semiprime ideal;

Language

English

Cited by

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