The q-theory of Finite Semigroups

• Main Authors: Rhodes, John. (Author), Steinberg, Benjamin. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston, MA : Springer US, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Computer science.; Algebra.; Group theory.; Group Theory and Generalizations.; Order, Lattices, Ordered Algebraic Structures.; General Algebraic Systems.; Mathematical Logic and Formal Languages.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/b104443

Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader  from the graduat...

Table of Contents:

• 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
• Author Index
• Index.