This comprehensive, encyclopedic text will provide the reader with a detailedunderstanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. It: (1) Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization; (2) Contains the only contemporary exposition of the complete theoryof the complexity of finite semigroups; (3) Introduces spectral theory into finite semigroup theory; (4) Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages; (5) Presents over 70 research problems, most new, and hundreds ofexercises. Additionally: (1) For newcomers, an appendix on elementary finite semigroup theory; (2) Extensive bibliography and index. The q-theory of FiniteSemigroups presents important techniques and results, many for the first timein book form, and thereby updates and modernizes the literature of semigroup theory. Redevelops the foundations of finite semigroup theory so that many major open problems fit into a single simple framework A new theory is developed.It provides a unifying approach to finite semigroup theory via quantization Many important techniques and results are clearly exposited in book form for the first time INDICE: Preface.- Introduction.- 1. Foundations for Finite Semigroup Theory.- 2. The q-operator.- 3.The Equational Theory.- 4. The Complexity of Finite Semigroups.- 5. Two-Sided Complexity and the Complexity of Operators.- 6. Algebraic Lattices, Continuous Lattices and Closure Operators.- 7. The Abstract Spectral Theory of PV.- 8. Quantales.- 9. The Triangular Product and Decomposition Results for Semirings.- A. The Green-Rees Local Structure Theory.- B. Tables on Preservation of Sups and Infs.- List of Problems.- References.- Table of Pseudovarieties.- Table of Operators and Products.- Index of Notation.- AuthorIndex.- Index.
- ISBN: 978-0-387-09780-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 690
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés
- Inicio /
- MATEMÁTICAS /
- ÁLGEBRA