Let $${{\mathfrak {F}}}_0$$F0 the class of fully zero-simple semihypergroups. In this paper, we study the main properties of residual semihypergroup $$(H_+, \star )$$(H+,⋆) of a semihypergroup $$(H, \circ )$$(H,∘) in… Click to show full abstract
Let $${{\mathfrak {F}}}_0$$F0 the class of fully zero-simple semihypergroups. In this paper, we study the main properties of residual semihypergroup $$(H_+, \star )$$(H+,⋆) of a semihypergroup $$(H, \circ )$$(H,∘) in $${{\mathfrak {F}}}_0$$F0. We prove that the quotient semigroup $$H_+/\beta ^*_{H_+}$$H+/βH+∗ is a completely simple and periodic semigroup. Moreover, we find the necessary and sufficient conditions for $$(H_+, \star )$$(H+,⋆) to be a torsion group and, in particular, an abelian 2-group.
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!