On Further Properties of Fully Zero-Simple Semihypergroups

Let $mfF_0$ the class of fully zero-simple semihypergroups. In this paper we study the main properties of residual semihypergroup $(H_+, star)$ of a semihypergroup $(H, circ)$ in $mfF_0$. We prove that the quotient semigroup $H_+/eta^*_{H_+}$ is a completely simple and periodic semigroup. Moreover, we find the necessary and sufficient conditions for $(H_+, star)$ to be a torsion group and, in particular, an Abelian $2$-group.