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 geome- tries,
characterized by Birkhoff as lattices of a special type, projec- tive,
descriptive and spherical geometries, represented by Prenowitz, as
multigroups, linear geometries and convex sets presented by Jan- tosciak
and Prenowitz as join spaces. As Prenowitz and Jantosciak did for
geometries, in this book we present and study several ma- thematical
disciplines that use the Hyperstructure Theory. Since the beginning, the
Hyperstructure Theory and particu- 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: - Fields by Krasner, Stratigopoulos
and Massouros Ch. - Lattices by Mittas, Comer, Konstantinidou,
Serafimidis, Leoreanu and Calugareanu - Rings by Nakano, Kemprasit,
Yuwaree - Quasigroups and Groupoids by Koskas, Corsini, Kepka, Drbohlav,
Nemec - Semigroups by Kepka, Drbohlav, Nemec, Yuwaree, Kempra- sit,
Punkla, Leoreanu - Ordered Structures by Prenowitz, Corsini, Chvalina IX
x - Combinatorics by Comer, Tallini, Migliorato, De Salvo, Scafati,
Gionfriddo, Scorzoni - Vector Spaces by Mittas - Topology by Mittas,
Konstantinidou - Ternary Algebras by Bandelt and Hedlikova.
