On Po-injective and Po-surjective Wreath Product of Pomonoids (European Journal of Pure and Applied Mathematics, 2025)
Let $R$ and $S$ be pomonoids and $_{R}{A}$ be a left $R$-poset. The wreath product of the pomonoids $R$ and $S$ by $_{R}{A}$ is defined as the pomonoid $T~=~R × F(A, S)$ While, the wreath product $_TC$ of the left $R$-poset $_{R}{A}$ with the left $S$-poset $_{S}{B}$ 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 $(r, f) \in R× F(A, S)$ and $ (a, b) \in 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.