Turkish Journal of Mathematics
DOI
10.3906/mat-1512-83
Abstract
In this paper, we introduce the concepts of order-congruences and strong order-congruences on an ordered semihypergroup $S,$ and obtain the relationship between strong order-congruences and pseudoorders on $S.$ Furthermore, we characterize the (strong) order-congruences by the $\rho$-chains, where $\rho$ is a (strong) congruence on $S.$ Moreover, we give a method of constructing order-congruences, and prove that every hyperideal $I$ of an ordered semihypergroup $S$ is congruence class of one order-congruence on $S$ if and only if $I$ is convex. Finally, we define and study the strong order-congruence generated by a strong congruence. As an application of the results of this paper, we solve an open problem on ordered semihypergroups given by Davvaz et al.
First Page
1255
Last Page
1271
Recommended Citation
TANG, JIAN; LUO, YANFENG; and XIE, XIANGYUN
(2018)
"A study on (strong) order-congruences in ordered semihypergroups,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 40.
https://doi.org/10.3906/mat-1512-83
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/40
