Applications of Hyperstructure Theory

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.

List of contents

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.

Product details

• Authors: Corsini, P Corsini, P. Corsini, V Leoreanu, V. Leoreanu
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.07.2009
• EAN: 9781402012228
• ISBN: 978-1-4020-1222-8
• No. of pages: 322
• Dimensions: 155 mm x 235 mm x 23 mm
• Weight: 672 g
• Illustrations: XII, 322 p.
• Series: Advances in Mathematics; Advances in Mathematics, Volume 5; Advances in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, C, Group Theory, Combinatorics, Mathematics and Statistics, Discrete Mathematics in Computer Science, Discrete Mathematics, Combinatorics & graph theory, Group Theory and Generalizations, Computer science—Mathematics, Maths for computer scientists, Mathematical logic, Mathematical Logic and Foundations, Mathematical foundations, Order, Lattices, Ordered Algebraic Structures, Ordered algebraic structures