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Commutativity and Completeness Degrees of Weakly Complete Hypergroups

Author

Listed:
  • Mario De Salvo

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy)

  • Dario Fasino

    (Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy)

  • Domenico Freni

    (Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy)

  • Giovanni Lo Faro

    (Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy)

Abstract

We introduce a family of hypergroups, called weakly complete, generalizing the construction of complete hypergroups. Starting from a given group G , our construction prescribes the β -classes of the hypergroups and allows some hyperproducts not to be complete parts, based on a suitably defined relation over G . The commutativity degree of weakly complete hypergroups can be related to that of the underlying group. Furthermore, in analogy to the degree of commutativity, we introduce the degree of completeness of finite hypergroups and analyze this degree for weakly complete hypergroups in terms of their β -classes.

Suggested Citation

  • Mario De Salvo & Dario Fasino & Domenico Freni & Giovanni Lo Faro, 2022. "Commutativity and Completeness Degrees of Weakly Complete Hypergroups," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:981-:d:774320
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    References listed on IDEAS

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    1. Gerasimos Massouros & Christos Massouros, 2020. "Hypercompositional Algebra, Computer Science and Geometry," Mathematics, MDPI, vol. 8(8), pages 1-33, August.
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    Cited by:

    1. Dario Fasino & Domenico Freni, 2023. "Preface to the Special Issue on “Hypergroup Theory and Algebrization of Incidence Structures”," Mathematics, MDPI, vol. 11(15), pages 1-3, August.

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