On quasi-prime, weakly quasi-prime left ideals in ordered-Γ-semigroups

Abstract

ABSTRACT. In this paper we obtain and establish some important results in ordered Γ-semigroups extending and generalizing those for semigroups given in [PETRICH, M.: Introduction to Semigroups, Merill, Columbus, 1973] . We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of ordered-Γ-semigroups. We also introduce the concept of weakly m-systems in ordered Γ-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by weakly m-systems.

The Concept of Dual of $\Gamma$-Ideals in a Co-ordered $\Gamma$-Semigroup with Apartness

“…To understand the notation and terminology, and to relate them to concepts in classical Γ-semigroup theory used in this article, which not previously described, the reader may look at the articles [11,12,16,17,39,40,42]. The idea of designing the concept of Γ-semigroups and some basic properties of this class of algebraic structures can be found in [17,39,40].…”

“…Fundamental information about the ordered Γ-semigroups can be found in papers [16,17]. Ideals in the ordered Γ-semigroups are discussed in the articles [12,42].…”

Convex ordered Gamma-semihypergroups associated to strongly regular relations

“…The notion of an ordered Γ-semigroup was first introduced by Sen and Seth [24] in 1993. Many authors studied different aspects of Γ-semigroups and ordered Γ-semigroups, for instance, Chinram and Tinpun [25], Hedayati [26], Hila [27], Kwon and Lee [28], and many others. The notion of Γ-H ν -semiring introduced by Hedayati and Davvaz in [29].…”

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