Classification of doubly distributive skew hyperfields and stringent hypergroups (Q1998974)

The notion of hyperfield is an immediate generalization of the notion of field. A hyperfield is stringent if the underlying additive hypergroup is. (i. e. \(a\boxplus b\) is a singleton whenever \(a \neq-b\).). In this paper, it is proved that every doubly distributive skew hyperfield is stringent, but not vice versa. Also, authors present a classification of stringent hypergroups. Moreover, It is proved that every stringent skew hyperfield is a quotient of a skew field.