Applications of Hyperstructure Theory

Applications of Hyperstructure Theory

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Some mathematical disciplines can be presented and developed in the context of other disciplines, for instance Boolean algebras, that Stone has converted in a branch of ring theory, projective geomeAs tries, characterized by Birkhoff as lattices of a special type, projecAs tive, descriptive and spherical geometries, represented by Prenowitz, as multigroups, linear geometries and convex sets presented by JanAs tosciak and Prenowitz as join spaces. As Prenowitz and Jantosciak did for geometries, in this book we present and study several maAs thematical disciplines that use the Hyperstructure Theory. Since the beginning, the Hyperstructure Theory and particuAs larly the Hypergroup Theory, had applications to several domains. Marty, who introduced hypergroups in 1934, applied them to groups, algebraic functions and rational fractions. New applications to groups were also found among others by Eaton, Ore, Krasner, Utumi, Drbohlav, Harrison, Roth, Mockor, Sureau and Haddad. Connections with other subjects of classical pure Mathematics have been determined and studied: a€c Fields by Krasner, Stratigopoulos and Massouros Ch. a€c Lattices by Mittas, Comer, Konstantinidou, Serafimidis, Leoreanu and Calugareanu a€c Rings by Nakano, Kemprasit, Yuwaree a€c Quasigroups and Groupoids by Koskas, Corsini, Kepka, Drbohlav, Nemec a€c Semigroups by Kepka, Drbohlav, Nemec, Yuwaree, KempraAs sit, Punkla, Leoreanu a€c Ordered Structures by Prenowitz, Corsini, Chvalina IX x a€c Combinatorics by Comer, Tallini, Migliorato, De Salvo, Scafati, Gionfriddo, Scorzoni a€c Vector Spaces by Mittas a€c Topology by Mittas , Konstantinidou a€c Ternary Algebras by Bandelt and Hedlikova.(8) We have (101)01= u z o x. Then from (1), ioiox = z6xox = u (z o zUx o x); now from (2) it follows x o x o x = u zo z, 26101 z6xox and finally from (3) we obtain (8) . (9) We have: (101)0(101) = u a o b = u ((a o a) U (6 o b)) = {a, 6}Cxox {o, 6}Cxoxanbsp;...

Title:Applications of Hyperstructure Theory
Author: P. Corsini, Violeta Leoreanu
Publisher:Springer Science & Business Media - 2003-03-31

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