Binary Relations on Ternary Semihypergroups

Abstract

Ternary semihypergroups are algebraic structures with one associative hyperoperation. The main propose of this article is to study binary relations on ternary semihypergroups and study some basic properties of compatible relations on them. In particular, we analyze the ternary hypergroup associated with a binary relation.

A physical example of algebraic hyperstructures: Leptons

“…We mention here another important book for the applications in Geometry and for the clearness of the exposition, written by W. Prenowitz and J. Jantosciak [13]. Another monograph is devoted especially to the study of Hyperring Theory, written by Davvaz and Leoreanu-Fotea [5]. It begins with some basic results concerning ring theory and algebraic hyperstructures, which represent the most general algebraic context, in which the reality can be modelled.…”

Operations on hyperideals in ordered Krasner hyperrings

“…The hyperstructure theory and its applications have been investigated by the contribution of many mathematicians. The principal notions of hyperstructure theory can be found in [9,10,11,12,14,29].…”

“…We recall some elementary definitions and results concerning Krasner hyperrings, which we need for development of our paper. The reader is referred to [14] for the notions and notations of hyperring theory. Section 3 is devoted to characterize the several properties of ordered Krasner hyperrings.…”

A note on composition (m, n)-hyperrings

“…Today one area of big interest for researchers working on algebraic hyperstructures is represented by the n-ary hyperstructures, since it has been proved they have many applications to computer science, coding theory, topology, combinatorics and quantum physic [9]. They are a generalization of classical algebraic hyperstructures, with a lot of applications in Euclidean and non Euclidean geometries, graphs and hypergraphs, binary relations, lattices, automata, cryptography, coding theory, artificial intelligence, probabilities, chemistry and so on (for more details see [3], [4], [9], [23]).…”

“…They are a generalization of classical algebraic hyperstructures, with a lot of applications in Euclidean and non Euclidean geometries, graphs and hypergraphs, binary relations, lattices, automata, cryptography, coding theory, artificial intelligence, probabilities, chemistry and so on (for more details see [3], [4], [9], [23]). …”