Turkish Journal of Mathematics




In the investigation of ordered $\Gamma$-hypersemigroups we often need counterexamples (of finite order) given by a table of multiplication and a figure that are impossible to make by hand and very difficult to write programs as well. So it is useful to have examples of ordered $\Gamma$-semigroups for which is much more easier to write programs and then from these examples to obtain corresponding examples of ordered $\Gamma$-hypersemigroups. In this respect we show that from every example of a regular, intra-regular, right (left) regular, right (left) quasi-regular, semisimple, right (left) simple, simple, strongly regular ordered $\Gamma$-semigroup given by a table of multiplication and an order, a corresponding example on ordered $\Gamma$-hypersemigroups can be obtained. From examples of different kind of ideals of ordered $\Gamma$-semigroups, corresponding examples of ordered $\Gamma$-hypersemigroups can be obtained. Examples illustrate the results.

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