The Transposition Axiom in Hypercompositional Structures

• exposé - matière potentielle : the theory of hypergroups
• exposé

1 The Transposition Axiom in Hypercompositional Structures Ch. G. Massouros1,3 and G. G. Massouros2,3 Abstract. This paper deals with the introduction of the transposition axiom into hypercompositional structures resulting from the hypergroup through the removal of certain axioms. Thus, the transposition hypergroupoid, transposition semi-hypergroup and transposition quasi-hypergroup are defined. It also deals with some issues of transposition hypergroups. Finally, it presents hypercompositional structures with internal or external compositions and hypercompositions, in which the transposition axiom is valid.

• transposition axiom
• g. g. massouros2
• hypercompositional structures
• hypergroup
• fields by sequences of such fields
• join hypergroup
• such structures
• creation