In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.

In this paper an extensive study of the concepts generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one see nature in class -ordered semigroups. Moreover we show that semigroup S is a if only complete semilattice completely π-regular Archimedean

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

Abstract A transformation of an ordered set M is isotone mapping into . By a representation semigroup S by transformations we mean homomorphism the , i.e. (since semigroup) from preserving operations. We prove that this type leads to “action” on and so introduce notion left operand over Also notions operator pseudoorder between operands show concept pseudoorders plays important role in study ho...

In this paper, the concepts of irreducible and strongly pseudo symmetric ideals in a partially ordered ternary semigroup are introduced. We also studied some interesting properties prove that space is topologized.

Most of the results on semigroups or ordered can be transferred to hypersemigroups hypersemigroups, respectively. The same, if we replace word "semigroup" by "groupoid", "hypersemigroup" "hypergroupoid". We show way pass from fuzzy hypersemigroups.

In this paper, we introduce the notions of interior filters, quasi-interior filters and weak-interior in a quasi-ordered semigroup. Additionally, study properties these types semigroups their interrelationships.

We consider the intuitionistic fuzzification of the concept of several ideals in an ordered semigroup S, and investigate some properties of such ideals. Mathematics Subject Classification: 06F35, 03G25, 03E72

Inverse semigroups form a variety of unary semigroups, that is, semigroups equipped with an additional unary operation, in this case a 7→ a−1. The theory of inverse semigroups is perhaps the best developed within semigroup theory, and relies on two factors: an inverse semigroup S is regular, and has semilattice of idempotents. Three major approaches to the structure of inverse semigroups have e...

In this note, we show in the line of [3] that an ordered Γ-semigroup is left and right simple if and only if it does not contain proper bi-ideals. Mathematics Subject Classification: 06F99