Abstract
ABSTRACTLet X be a finite chain. Denote by 𝒪(X) the monoid of all order-preserving full transformations on X. For any nonempty convex subchain Y of X, let Then is a submonoid of 𝒪(X).In this paper, we characterize Green’s relations and Green’s *-relations on . Then we prove that is abundant but not regular. Furthermore, we describe the regular elements of and determine when is a regular semigroup. In addition, we compute the cardinalities of , and , respectively.
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