Study of Properties of Several Kinds of Hyperideals in Ordered Ternary Semihypergroups

Thawhat Changphas, Bijan Davvaz

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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References


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DOI: https://doi.org/10.22342/jims.27.2.965.228-239

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