A further study on ordered regular equivalence relations in ordered semihypergroups-Reference-Cited by-同舟云学术

A further study on ordered regular equivalence relations in ordered semihypergroups

Published:2018-01-01 Issue:1 Volume:16 Page:168-184
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Tang Jian¹,Feng Xinyang²,Davvaz Bijan³,Xie Xiang-Yun⁴

Affiliation:

1. School of Mathematics and Statistics , Fuyang Normal University , Fuyang , Anhui, 236037 , China

2. School of Mathematics and Statistics , Lanzhou University , Lanzhou , Gansu, 730000 , China

3. Department of Mathematics , Yazd University , Yazd , Iran

4. School of Mathematics and Computational Science , Wuyi University , Jiangmen , Guangdong, 529020 , China

Abstract

Abstract In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2018-0016/pdf

Reference28 articles.

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