Some ordered hypersemigroups which enter their properties into their σ-classes

Document Type : Research Paper

Author

Department of Mathematics, University of Athens, P.O.Box 16784, Athens, Greece

Abstract

An important problem in the theory of ordered hypersemigroups is to describe the ordered hypersemigroups which enter their properties into their σ-classes. In this respect, we prove the following: If H is a regular, left (right) regular, completely regular, intra-regular, left (right) quasi-regular, semisimple, k regular, archimedean, weakly commutative, left (right) simple, simple, left (right) strongly simple ordered semigroup and σ a complete semilattice congruence on H then, for each a ∈ H, the σ-class (a)σ of H is, respectively, so.

Keywords


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