On ordered Γ-hypersemigroups, minimal bi-ideals, and minimal left ideals

The definition of ordered Γ-hypersemigroups and the definitions of regular and intra-regular ordered Γhypersemigroups in the existing bibliography should be corrected. Care should be given to the definitions of bi-Γhyperideals and quasi-Γ-hyperideals as well. The main results are a characterization of minimal bi-ideals of an orderedΓ-hypersemigroup S in terms of B-simple bi-ideals of S and a characterization of minimal left (resp. right) ideals ofan ordered Γ-hypersemigroup S in terms of left (resp. right) simple subsemigroups of S

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[1] Cao Y, Xu X. On minimal and maximal left ideals in ordered semigroups. Semigroup Forum 2000; 60 (2): 202-207. doi: 10.1007/s002339910014
[2] Iampan A. Characterizing ordered bi-ideals in ordered Γ-semigroups. Iranian Journal of Mathematical Sciences and Informatics 2009; 4 (1): 17-25. doi: 10.7508/ijmsi.2009.01.002
[3] Kehayopulu N. On ordered Γ-semigroups. Scientiae Mathematicae Japonicae 2010; 71 (2): 179-185. doi: 10.32219/isms.71.2.179
[4] Kehayopulu N. On regular duo po-Γ-semigroups. Mathematica Slovaca 2011; 61 (6): 871–884.
[5] Kehayopulu N. On bi-ideals of ordered Γ-semigroups –A Corrigendum. Hacettepe Journal of Mathematics and Statistics 2013; 42 (5): 559-567.
[6] Kehayopulu N. An application of Γ-semigroups techniques to the Green’s theorem. Afrika Matematika 2018; 29 (1-2): 65-71. doi: 10.1007/s13370-017-0526-4
[7] Kehayopulu N. Erratum to “Study on quasi-Γ-hyperideals in Γ-semihypergroups”. Turkish Journal of Mathematics 2020; 44 (3): 957-959. doi: 10.3906/mat-2003-37
[8] Kehayopulu N. Erratum to: “Application of (m, n)-Γ-hyperideals on characterization of LA-Γ-hypersemigroups” by Abul Basar. Discussiones Mathematica General Algebra and Applications 2020; 40 (1): 135-138. doi: 10.7151/dmgaa.1329
[9] Kehayopulu N. Lattice ordered semigroups and Γ-hypersemigroups. Turkish Journal of Mathematics 2020; 44 (5): 1835-1851. doi:10.3906/mat-1909-83
[10] Xu X, Ma J. A note on minimal bi-ideals in ordered semigroups. Southeast Asian Bulletin of Mathematics 2003; 27 (1): 149-154.