Commutative hypergroups associated with a hyperfield
Herbert Heyer, Satoshi Kawakami, Tatsuya Tsurii, Satoe Yamanaka
TL;DR
This paper introduces a new class of commutative hypergroups linked to hyperfields of compact hypergroups, explores their dual structures, and examines related hypergroups, expanding the theoretical framework of hypergroup theory.
Contribution
It presents the first construction of commutative hypergroups associated with hyperfields of compact hypergroups and analyzes their dual relations.
Findings
Established the dual hyperfield structure
Connected hypergroups related to hyperfield pairs
Extended hypergroup theory with new algebraic structures
Abstract
In the present paper we introduce a commutative hypergroup associated with a hyperfield of a compact commutative hypergroup based on a discrete commutative hypergroup. Moreover we investigate the dual hyperfield and show the dual relation. As an application we study some hypergroups related to a pair of commutative hypergroups.
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