## Turkish Journal of Mathematics

#### DOI

10.3906/mat-2111-33

#### Abstract

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.

#### Keywords

Ordered $\Gamma$-semigroup, ordered $\Gamma$-hypersemigroup, ideal, regular, intra-regular, semisimple

#### First Page

323

#### Last Page

337

#### Recommended Citation

KEHAYOPULU, NIOVI
(2022)
"Finite ordered $\Gamma$-hypersemigroups constructed by ordered $\Gamma$-semigroups,"
*Turkish Journal of Mathematics*: Vol. 46:
No.
1, Article 22.
https://doi.org/10.3906/mat-2111-33

Available at:
https://journals.tubitak.gov.tr/math/vol46/iss1/22