TY - JOUR
ID - 87415
TI - $(m,n)$-Hyperideals in Ordered Semihypergroups
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Mahboob, Ahsan
AU - Khan, Noor Mohammad
AU - Davvaz, Bijan
AD - Aligarh Muslim University
AD - Yazd University
Y1 - 2020
PY - 2020
VL - 12
IS - 1
SP - 43
EP - 67
KW - Ordered semihypergroups
KW - $(m,0)$-hyperideals
KW - $(0,n)$-hyperideals
DO - 10.29252/cgasa.12.1.43
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_87415.html
L1 - https://cgasa.sbu.ac.ir/article_87415_1fd525cccd124d58a33309087242f95f.pdf
ER -