On ordered hypersemigroups given by a table of multiplication and a figure

Authors: NIOVI KEHAYOPULU

Abstract: The aim is to show that from every example of a regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered semigroup given by a table of multiplication and an order, a corresponding example of regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered hypersemigroup can be constructed having the same left (right) ideals, bi-ideals, quasi-ideals, or interior ideals. On this occasion, some further related results have also been given.

Keywords: Ordered semigroup, ordered hypersemigroup, right (left) ideal, bi-ideal, quasi-ideal, interior ideal, regular, right (left) regular, intraregular, right (left) quasiregular, semisimple, right (left) simple, simple

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