Green's relations on ordered n-ary semihypergroups

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.


In this paper, we introduce the concept of weak $i$-hyperfilters of ordered $n$-ary
semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and then discuss their
related properties. We define the Green’s relations $M_i, J , H$ and $K$ on ordered $n$-ary
semihypergroups and investigate the relationships between the Green’s relations and the
equivalence relation $W_i$, which is generated by the weak $i$-hyperfilters. Also, we give
the characterizations of intra-regular ordered $n$-ary semihypergroups via the properties
of weak $i$-hyperfilters. Finally, we introduce the concepts of $(i-, Λ-)$duo ordered $n$-ary
semihypergroups and establish some interesting properties.


Main Subjects

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