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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3414

Abstract

The results on $\Gamma$-hypersemigroups are obtained either as corollaries of corresponding results on $\vee e$ or $poe$-semigroups or on the line of the corresponding results on $le$-semigroups. It has come to our attention that Theorem 3.22 in [4] cannot be obtained as corollary to Theorem 2.2 of the same paper as for a $\Gamma$-hypersemigroup, $({\cal P}^*(M),\Gamma,\subseteq)$ is a $\vee e$-semigroup and not an $le$-semigroup. Also on p. 1850, l. 12 in [4], the "$le$-semigroup" should be changed to "$\vee e$-semigroup". In the present paper we prove Theorems 3.26 and 3.28 stated without proof in [4]. On this occasion, some further results are given to emphasize what we say. The results on $\Gamma$-hypersemigroups are obtained from the more abstract structure of the $poe$-semigroups. Further investigation on $poe$-semigroups and $le$-semigroups is interesting.

Keywords

$\Gamma$-hypersemigroup, $le$-semigroup, intra-regular, right regular, bi-ideal element, bi-ideal

First Page

1087

Last Page

1098

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