(untitled) (European Journal of Pure and Applied Mathematics, 2025)
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), (P_E), and strongly flat have been examined on the wreath product _TC and the relations among them have also been established.