@article{Daengsaen2022, 
author = {Jukkrit Daengsaen and Sorasak Leeratanavalee},
title = {Semilattice strongly regular relations on ordered    n-ary semihypergroups},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {478-498},
keywords = {ordered semihypergroup, n-ary semihypergroup, hyperideal, hyperfilter},
url = {https://www.sciopen.com/article/10.3934/math.2022031},
doi = {10.3934/math.2022031},
abstract = {In this paper, we introduce the concept of    j-hyperfilters, for all positive integers    1  ≤  j  ≤  n and    n  ≥  2, on (ordered)    n-ary semihypergroups and establish the relationships between    j-hyperfilters and completely prime    j-hyperideals of (ordered)    n-ary semihypergroups. Moreover, we investigate the properties of the relation        N  , which is generated by the same principal hyperfilters, on (ordered)    n-ary semihypergroups. As we have known from [21] that the relation        N   is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on    n-ary semihypergroups where    n  ≥  3. However, we provide a sufficient condition that makes the previous conclusion true on    n-ary semihypergroups and ordered    n-ary semihypergroups where    n  ≥  3. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their        N  -classes. As an application of the results, a related problem posed by Tang and Davvaz in [31] is solved.}
}