An investigation on hyperS-posets over ordered semihypergroups

Jian Tang, Bijan Davvaz, and Xiang-Yun Xie. "An investigation on hyperS-posets over ordered semihypergroups." Open Mathematics 15.1 (2017): 37-56. <http://eudml.org/doc/288008>.

@article{JianTang2017,
abstract = {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.},
author = {Jian Tang, Bijan Davvaz, Xiang-Yun Xie},
journal = {Open Mathematics},
keywords = {Ordered semihypergroup; Hyper S-poset; (Strong) order-congruence; Pseudoorder; ρ-chain; ordered semihypergroup; hyper $S$-poset; (strong) order-congruence; pseudoorder; $\rho $-chain},
language = {eng},
number = {1},
pages = {37-56},
title = {An investigation on hyperS-posets over ordered semihypergroups},
url = {http://eudml.org/doc/288008},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Jian Tang
AU - Bijan Davvaz
AU - Xiang-Yun Xie
TI - An investigation on hyperS-posets over ordered semihypergroups
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 37
EP - 56
AB - 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.
LA - eng
KW - Ordered semihypergroup; Hyper S-poset; (Strong) order-congruence; Pseudoorder; ρ-chain; ordered semihypergroup; hyper $S$-poset; (strong) order-congruence; pseudoorder; $\rho $-chain
UR - http://eudml.org/doc/288008
ER -