Left-m-filter, Right-n-filter and (m,n)-filter on Ordered Semigroup
Noor Mohammad Khan, Ahsan Mahboob · Journal of Taibah University for Science · 2018
In this paper, as a generalization of the concepts of left filters, right filters and filters of ordered semigroups, the concepts, for any positive integers m and n, of left-m-filters, right-n-filters and (m,n)-filters in ordered semigroups have been introduced and some properties of these generalized notions have been investigated. Finally left-m-filters (resp. right-n-filters, (m,n)-filters) of (m,0)-regular (resp. (0,n)-regular, (m,n)-regular) ordered semigroups have been characterized in terms of its prime generalized (m,0)-ideals (resp. (0,n)-ideals, (m,n)-ideals).