On Further Properties of Fully Zero-Simple Semihypergroups

Abstract

Let $${{\mathfrak {F}}}_0$$ 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 $${{\mathfrak {F}}}_0$$ . We prove that the quotient semigroup $$H_+/\beta ^*_{H_+}$$ 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.