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" Applications of Hyperstructure Theory "
by Piergiulio Corsini, Violeta Leoreanu.
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BL
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573154
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b402373
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| Main Entry
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Corsini, Piergiulio.
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Applications of Hyperstructure Theory\ by Piergiulio Corsini, Violeta Leoreanu.
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| Publication Statement
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Boston, MA :: Springer US :: Imprint: Springer,, 2003.
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| Series Statement
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Advances in Mathematics ;; 5
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9781475737141
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: 9781441952455
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| Contents
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Basic notions and results on Hyperstructure Theory -- 1 Some topics of Geometry -- 2 Graphs and Hypergraphs -- 3 Binary Relations -- 4 Lattices -- 5 Fuzzy sets and rough sets -- 6 Automata -- 7 Cryptography -- 8 Codes -- 9 Median algebras, Relation algebras, C-algebras -- 10 Artificial Intelligence -- 11 Probabilities.
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| Abstract
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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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Mathematics.
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Computational complexity.
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Group theory.
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Algebra.
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Combinatorics.
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Logic, Symbolic and mathematical.
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Leoreanu, Violeta.
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SpringerLink (Online service)
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