On Quasi-gamma-ideals in Gamma-semigroups

Ronnason Chinram*

ABSTRACT: The concept of quasi-ideals in semigroups was introduced in 1956 by O. Steinfeld. The class of quasi-ideals in semigroups is a generalization of one-sided ideals in semigroups. It is well-known that the intersection of a left ideal and a right ideal of a semigroup S is a quasi-ideal of S and every quasi-ideal of S can be obtain in this way. In 1981, M. K. Sen have introduced the concept of Γ-semigroups. One can see that Γ- semigroups are a generalization of semigroups. In this research, quasi-Γ-ideals in Γ-semigroups are introduced and some properties of quasi-Γ-ideals in Γ-semigroups are provided.

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Department of Mathematics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, 90112, Thailand.

* Corresponding author, E-mail: ronnason.c@psu.ac.th

Received 18 Jan 2006, Accepted 10 May 2006