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

Title & Authors
ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS
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) $\small{\Gamma}$-semigroups. In 1981, Sen [8] has introduced the concept of the $\small{\Gamma}$-semigroups. We can see that any semigroup can be considered as a $\small{\Gamma}$-semigroup. The concept of ordered ideal extensions in ordered $\small{\Gamma}$-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 $\small{\Gamma}$-semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered $\small{\Gamma}$-semigroups.
Keywords
(ordered) semigroup;(ordered) $\small{\Gamma}$-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
1.
ROUGH PRIME IDEALS AND ROUGH FUZZY PRIME IDEALS IN GAMMA-SEMIGROUPS,;

대한수학회논문집, 2009. vol.24. 3, pp.341-351
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