On Po-injective and Po-surjective Wreath Product of Pomonoids

Let R and S be pomonoids and RA be a left R-poset. The wreath product of the pomonoids R and S by RA is defined as the pomonoid T~=~R × F(A, S) While, the wreath product TC of the left R-poset RA with the left S-poset SB over the pomonoid T= R × F(A, S) is the left T-poset T C= R A× S B endowed with the monotone action given by $(r, f)(a, b) = (ra, f(a)b),$ where (r, f) ∈ R× F(A, S) and (a, b) ∈ A× B. The po-injectivity and po-cancellative properties on the wreath product TC are studied and the relations between them are established. The relation between po-surjective property and other properties on the wreath product TC are also established. Finally the characterization of some properties of po-flatness such as po-torsion free, properties $(P)$, $(E)$, (PE), and strongly flat have been examined on the wreath product TC and the relations among them have also been established.