In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S-poset A, and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize the (strong) order-congruences by the ρ-chains, where ρ is a (strong) congruence on A. Moreover, we give a method of constructing order-congruences, and prove that every hyper S-subposet B of a hyper S-poset A is a congruence class of one order-congruence on A if and only if B is convex. In the sequel, we give some homomorphism theorems of hyper S-posets, which are generalizations of similar results in S-posets and ordered semigroups.
@article{bwmeta1.element.doi-10_1515_math-2017-0004,
author = {Jian Tang and Bijan Davvaz and Xiang-Yun Xie},
title = {An investigation on hyperS-posets over ordered semihypergroups},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {37-56},
zbl = {06699450},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0004}
}
Jian Tang; Bijan Davvaz; Xiang-Yun Xie. An investigation on hyperS-posets over ordered semihypergroups. Open Mathematics, Tome 15 (2017) pp. 37-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0004/