@article {
author = {Mahboob, Ahsan and Khan, Noor and Davvaz, Bijan},
title = {$(m,n)$-Hyperideals in Ordered Semihypergroups},
journal = {Categories and General Algebraic Structures with Applications},
volume = {12},
number = {1},
pages = {43-67},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.12.1.43},
abstract = {In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideals, respectively. The relations ${_m\mathcal{I}}, \mathcal{I}_n, \mathcal{H}_m^n$, and $\mathcal{B}_m^n$ on an ordered semihypergroup are, then, introduced. We prove that $\mathcal{B}_m^n \subseteq \mathcal{H}_m^n$ on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the $(m,0)$-regularity [$(0,n)$-regularity] of an element induce the $(m,0)$-regularity [$(0,n)$-regularity] of the whole $\mathcal{H}_m^n$-class containing that element as well as the fact that $(m,n)$-regularity and $(m,n)$-right weakly regularity of an element induce the $(m,n)$-regularity and $(m,n)$-right weakly regularity of the whole $\mathcal{B}_m^n$-class and $\mathcal{H}_m^n$-class containing that element, respectively.},
keywords = {Ordered semihypergroups,$(m,0)$-hyperideals,$(0,n)$-hyperideals},
url = {https://cgasa.sbu.ac.ir/article_87415.html},
eprint = {https://cgasa.sbu.ac.ir/article_87415_1fd525cccd124d58a33309087242f95f.pdf}
}