Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 19 1 2023 08 01 Green's relations on ordered n-ary semihypergroups 143 167 103858 10.48308/cgasa.19.1.143 EN Jukkrit Daengsaen Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand. Sorasak Leeratanavalee Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand. 0000-0001-8818-6134 Journal Article 2023 04 21 In this paper, we introduce the concept of weak $i$-hyperfilters of ordered $n$-ary<br />semihypergroups, where a positive integer 1 ≤ i ≤ n and n ≥ 2, and then discuss their<br />related properties. We define the Green’s relations $M_i, J , H$ and $K$ on ordered $n$-ary<br />semihypergroups and investigate the relationships between the Green’s relations and the<br />equivalence relation $W_i$, which is generated by the weak $i$-hyperfilters. Also, we give<br />the characterizations of intra-regular ordered $n$-ary semihypergroups via the properties<br />of weak $i$-hyperfilters. Finally, we introduce the concepts of $(i-, Λ-)$duo ordered $n$-ary<br />semihypergroups and establish some interesting properties. https://cgasa.sbu.ac.ir/article_103858_ee747fb8ead4ffd91ecbfd0708d73a5e.pdf