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.
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Acknowledgements
The work of M. De Salvo, D. Freni, and G. Lo Faro has been partially supported by INDAM (GNSAGA). D. Freni is supported by PRID 2017 funding (DMIF, University of Udine).
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De Salvo, M., Freni, D. & Faro, G.L. On Further Properties of Fully Zero-Simple Semihypergroups. Mediterr. J. Math. 16, 48 (2019). https://doi.org/10.1007/s00009-019-1324-z
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DOI: https://doi.org/10.1007/s00009-019-1324-z