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Submitted
October 18, 2020
Accepted
July 20, 2021
Published
July 22, 2021
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Abstract

A non-empty subset S together with an associative function f from S × S×S into the family of all non-empty subsets of S is called a ternary semihypergroup. In this paper, we consider a semihypergroup (S, f) besides a binary relation ≤, where ≤ is a partial order relation on S such that satisfies the monotone condition. This structure is called an ordered ternary semihypergroup. We introduce and investigate the notions of bi-hyperideal and quasi-hyperideal in ordered ternary semihyperroups. In particular, we prove that an ordered ternary semihypergroup is left and right simple if and only if it does not contain proper bi-hyperideals

Keywords

Algebraic hyperstructure ordered ternary semihypergrouip ternary subsemihypergroup (bi- quasi-) hyperideal prime hyperideal quasi-simple.

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Changphas, T., & Davvaz, B. (2021). Study of Properties of Several Kinds of Hyperideals in Ordered Ternary Semihypergroups. Journal of the Indonesian Mathematical Society, 27(2), 228–239. https://doi.org/10.22342/jims.27.2.965.228-239
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