Structural properties for (m,n)quasihyperideals in ordered semihypergroups
A. Mahboob, N. M. Khan, B. Davvaz
In this paper, we first introduce the notion of an (m,n)quasihyperideal
in an ordered semihypergroup and, then, study some properties of (m,n)quasihyperideals
for any positive integers m and n. Thereafter, we characterize the minimality
of an (m,n)quasihyperideal in terms of (m,0)hyperideals and (0,n)hyperideals respectively.
The relation Ǫ_{m}^{n} on an ordered semihypergroup is, then, introduced for any positive
integers m and n and proved that the relation Ǫ_{m}^{n} is contained in the relation
Ǫ=Ǫ_{1}^{1}. We also show that, in an (m,n)regular ordered semihypergroup,
the relation Ǫ_{m}^{n} coincides with the relation Ǫ. Finally, the notion of
an (m,n)quasihypersimple ordered semihypergroup is introduced and some properties of
(m,n)quasihypersimple ordered semihypergroups are studied. We further show that, on any
(m,n)quasihypersimple ordered semihypergroup, the relations Ǫ_{m}^{n} and
Ǫ are equal and are universal relations.
Tbilisi Mathematical Journal, Vol. 11(4) (2018), 145163
