The author makes an important contribution to hyperstructure theory. He characterizes the feebly canonical hypergroups as K_H-hypergroups, where H is canonical. Feebly canonical hypergroups, introduced and analysed by the reviewer in 1982, generalize the notions of canonical and of complete hypergroups. A hypergroup H is called feebly canonical if it is regular, reversible, commutative and if, for every pair of inverses x ′ , x ′′ , of an element x and any a∈H , a∘x ′ =a∘x ′′ . Other topics of the paper are the construction of two classes of feebly quasicanonical hypergroups (i.e. hypergroups satisfying the same conditions as feebly canonical hypergroups except for commutativity) and the determination of the number of distinct feebly canonical hypergroups whose underlying set is partitioned in at most three classes by an opportune equivalence relation.
Feebly canonical hypergroups
DE SALVO, Mario
1990-01-01
Abstract
The author makes an important contribution to hyperstructure theory. He characterizes the feebly canonical hypergroups as K_H-hypergroups, where H is canonical. Feebly canonical hypergroups, introduced and analysed by the reviewer in 1982, generalize the notions of canonical and of complete hypergroups. A hypergroup H is called feebly canonical if it is regular, reversible, commutative and if, for every pair of inverses x ′ , x ′′ , of an element x and any a∈H , a∘x ′ =a∘x ′′ . Other topics of the paper are the construction of two classes of feebly quasicanonical hypergroups (i.e. hypergroups satisfying the same conditions as feebly canonical hypergroups except for commutativity) and the determination of the number of distinct feebly canonical hypergroups whose underlying set is partitioned in at most three classes by an opportune equivalence relation.Pubblicazioni consigliate
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