The q-theory of Finite Semigroups

• Main Authors: Rhodes, John (Author), Steinberg, Benjamin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Mathematical logic.; Algebra.; Group theory.; Ordered algebraic structures.; Group Theory and Generalizations.; Order, Lattices, Ordered Algebraic Structures.; General Algebraic Systems.; Mathematical Logic and Formal Languages.

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:

• I The q operator and Pseudovarieties of Relational Morphisms
• Foundations for Finite Semigroup Theory
• The q-operator
• The Equational Theory
• II Complexity in Finite Semigroup Theory
• The Complexity of Finite Semigroups
• Two-Sided Complexity and the Complexity of Operators
• III The Algebraic Lattice of Semigroup Pseudovarieties
• Algebraic Lattices, Continuous Lattices and Closure Operators
• The Abstract Spectral Theory of PV
• IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product
• Quantales
• The Triangular Product and Decomposition Results for Semirings.