A physical example of algebraic hyperstructures: Leptons

Abstract

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.

Contribution to study special kinds of hyperideals in ordered semihyperrings

“…Another motivation for the study of hyperstructures comes from physical phenomenon as the nuclear fission. This motivation and the results were presented by Hošková, Chvalina and Račková (see [22]) and Davvaz et al [23]. Many authors used to focus their research on ordered semihypergroups.…”

On fuzzy hyper B-ideals of hyper B-algebras

“…The hyperstructure theory was introduced by F. Marty [8] during the 8th Congress of Scandinavian Mathematicians in 1934. This attracted the interest of many researchers because of its wide applications in various fields of mathematics and other scientific disciplines such as chemistry, biology and physics found in [2,3,4].…”

The associated hyperringoid to a Krasner hyperring

“…The applications of hyperstructures to other areas have been extensively studied such as optimization theory, graph theory, physics, chemistry, theory of discrete event dynamical systems, generalized fuzzy computation, automata theory, formal language theory, coding theory and analysis of computer programs, for example, see [4][5][6].…”