$(m,n)$-Hyperfilters in Ordered Semihypergroups

Ahsan Mahboob, Noor Mohammad Khan

First, we generalize concepts of left hyperfilters, right hyperfilters and hyperfilters of an ordered semihypergroup by introducing concepts of left-$m$-hyperfilters, right-$n$-hyperfilters and $(m,n)$-hyperfilters of an ordered semihypergroup. Then, some properties of these generalized hyperfilters have been studied. Finally, left-$m$-hyperfilters (resp. right-$n$-hyperfilters, $(m,n)$-hyperfilters) of $(m,0)$-regular (resp. $(0,n)$-regular, $(m,n)$-regular) ordered semihypergroups characterize in terms of their completely prime generalized $(m,0)$-hyperideals (resp. $(0,n)$-hyperideals, $(m,n)$-hyperideals).