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In this paper, we first define various types of k-regularity of ordered semigroups and various types of k-Archimedness of ordered semigroups. Also, we define the relations τ (k) , τ (k) l , τ (k) r , τ (k) t and τ (k) b (k ∈ Z + ) on an ordered semigroup. Using these notions, filter, and radical subsets of an ideal, left ideal and biideal of ordered semigroups we describe chains of k-Archimedean (left k-Archimedean, t-k-Archimedean) ordered subsemigroups.doi:10.2298/fil1610771q fatcat:gkiawaei4rbc3mknmwjajgr3pe