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Applications of Hyperstructure Theory (Paperback, Softcover reprint of hardcover 1st ed. 2003)
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Applications of Hyperstructure Theory (Paperback, Softcover reprint of hardcover 1st ed. 2003)
Series: Advances in Mathematics, 5
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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 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.
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