On properties $\gamma_d^{(n)}$ in a semihypergroup with a unique zero element

Let (S; ·) be a semihypergroup with the unique zero element 0. Here, we study some properties of S in which 0 plays an important role, and obtain some results to explain some relationships among these properties. As a main result, we prove every 2 −FN semihypergroup satisfying $\gamma_2^{(4)}$ satisfies $\gamma^{(2)}$, $\gamma^{(3)}$, and $\gamma^{(4)}$