Commutativity and Completeness Degrees of Weakly Complete Hypergroups

Mario De Salvo, Dario Fasino, Domenico Freni and Giovanni Lo Faro
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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

Mathematics, 2022, vol. 10, issue 6, 1-17

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.

Keywords: hypergroups; complete hypergroup; fundamental relations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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