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On Further Properties of Fully Zero-Simple Semihypergroups

  • Mario De Salvo
  • Domenico FreniEmail author
  • Giovanni Lo Faro
Article
  • 20 Downloads

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.

Keywords

Semihypergroups simple semihypergroups fully semihypergroups 

Mathematics Subject Classification

20N20 05A99 

Notes

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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Copyright information

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Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche e Informatiche Scienze Fisiche e Scienze della TerraUniversità di MessinaMessinaItaly
  2. 2.Dipartimento di Scienze Matematiche Informatiche e FisicheUniversità di UdineUdineItaly

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