# An investigation on hyperS-posets over ordered semihypergroups

Jian Tang; Bijan Davvaz; Xiang-Yun Xie

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 37-56
- ISSN: 2391-5455

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topJian 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 -

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