Maximal Idempotent-Generated Subsemigroups of Semigroup Oεn

Key words: 
• order-preserving、maximal subsemigroup、maximal idempotent-generated subsemigroup

Abstract: Let Oεn be the semigroup of all increasing and order-preserving full transformations on Xn .For arbitrary n such that n≥3 ,the structures of the maximal idempotent-generated subsemigroups of the sem-igroup Oεn were studied .The authors have proved that the semigroup Oεn has exactly two classes of maxi-mal idempotent-generated subsemigroups :S=Oεn\{∈}and S= In-2 ∪{∈}∪ Gm(1≤ m≤ n-1) ,where In-2 ={α∈Oεn :|im(α)| ≤ n-2},Gm={α∈Oεn :|im(α)|= n-1 ,mα= m},∈is the identity on Xn .