Commutative hypergroups associated with a hyperfield
  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. 
Herbert Heyer, Satoshi Kawakami, Tatsuya Tsurii and Satoe Yamanaka
math.FA