Morita equivalence for partially ordered monoids and po-Γ-semigroups with unities

Abstract

We prove that operator pomonoids of a po-Γ-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if L and R are Morita equivalent pomonoids then a po-Γ-semigroup A with unities can be constructed such that left and right operator pomonoids of A are Pos-isomorphic to L and R respectively. Using this nice connection between po-Γ-semigroups and Morita equivalence for pomonoids we, in one hand, obtain some Morita invariants of pomonoids using the results of po-Γ-semigroups and on the other hand, some recent results of Morita theory of pomonoids are used to obtain some results of po-Γ-semigroups.