Applications of Hyperstructure Theory

1. Auflage. Softcover version of original hardcover Auflage 2003
ISBN: 978-1-4419-5245-5
Verlag: Springer US

Buch, Englisch, Band 5, 322 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 517 g

Reihe: Advances in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Leoreanu, V.

Corsini, P.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Kryptologie, Informationssicherheit

Inhaltsverzeichnis

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.