An investigation on hyperS-posets over ordered semihypergroups

• Autorzy: Jian Tang , Bijan Davvaz , Xiang-Yun Xie
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Ordered semihypergroup; Hyper S-poset; (Strong) order-congruence; Pseudoorder; ρ-chain

Kategorie tematyczne

• 20N20: Hypergroups
• 06F05: Ordered semigroups and monoids
• 20M30: Representation of semigroups; actions of semigroups on sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 37-56

Daty

wydano

2017-01-01

otrzymano

2016-04-27

zaakceptowano

2016-11-22

online

2017-02-16

Twórcy

autor

Jian Tang

• School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, 236037,

autor

Bijan Davvaz

• Department of Mathematics, Yazd University, Yazd,

autor

Xiang-Yun Xie

• School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong, 529020,

Identyfikatory

DOI

10.1515/math-2017-0004