Characterization of Ordered Semihypergroups by Covered Hyperideals

After introducing the notions of the Green’s relation J, hyper J-class and covered hyperideal in an ordered semihypergroup, some important properties of the hyper J-class and covered hyperideals are studied. Then maximal and minimal hyperideals of an ordered semihypergroup are defined and some vital...

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Published inKragujevac Journal of Mathematics Vol. 47; no. 3; pp. 417 - 429
Main Authors ALI, MD FIROJ, KHAN, NOOR MOHAMMAD
Format Journal Article
LanguageEnglish
Published 2023
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Summary:After introducing the notions of the Green’s relation J, hyper J-class and covered hyperideal in an ordered semihypergroup, some important properties of the hyper J-class and covered hyperideals are studied. Then maximal and minimal hyperideals of an ordered semihypergroup are defined and some vital results have been proved. We also define a hyperbase of an ordered semihypergroup and prove the existence of a hyperbase under certain conditions in an ordered semihypergroup. In an ordered semihypergroup, after defining the greatest covered hyperideal and the greatest hyperideal, some results about these hyperideals are proved. Finally, in a regular ordered semihypergroup, we show that, under some conditions, each hyperideal is also a covered hyperideal.
ISSN:1450-9628
2406-3045
DOI:10.46793/KgJMat2303.417A