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

• Siripitukdet, Manoj ;
• Iampan, Aiyared
• Published : 2008.01.31
• 92 11

#### 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) $\Gamma$-semigroups. In 1981, Sen [8] has introduced the concept of the $\Gamma$-semigroups. We can see that any semigroup can be considered as a $\Gamma$-semigroup. The concept of ordered ideal extensions in ordered $\Gamma$-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 $\Gamma$-semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered $\Gamma$-semigroups.

#### Keywords

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

#### References

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