# A further study on ordered regular equivalence relations in ordered semihypergroups

A further study on ordered regular equivalence relations in ordered semihypergroups AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

# A further study on ordered regular equivalence relations in ordered semihypergroups

, Volume 16 (1): 17 – Mar 20, 2018
17 pages

/lp/de-gruyter/a-further-study-on-ordered-regular-equivalence-relations-in-ordered-LRNNrvxg2h
Publisher
de Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0016
Publisher site
See Article on Publisher Site

### Abstract

AbstractIn 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.

### Journal

Open Mathematicsde Gruyter

Published: Mar 20, 2018

Keywords: Ordered semihypergroup; Weak pseudoorder; Ordered regular equivalence relation; 20N20; 06F05; 20M12

### References

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