Morita equivalence for partially ordered monoids and po-\(\Gamma\)-semigroups with unities

Abstract

We prove that operator pomonoids of a po-\(\Gamma\)-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if \(L\) and \(R\) are Morita equivalent pomonoids then a po-\(\Gamma\)-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-\(\Gamma\)-semigroups and Morita equivalence for pomonoids we, in one hand, obtain some Morita invariants of pomonoids using the results of po-\(\Gamma\)-semigroups and on the other hand, some recent results of Morita theory of pomonoids are used to obtain some results of po-\(\Gamma\)-semigroups.