The q-theory of Finite Semigroups

  • John Rhodes
  • Benjamin Steinberg
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages 1-30
  2. The q-operator and Pseudovarieties of Relational Morphisms

    1. Front Matter
      Pages 1-1
  3. Part I The q operator and Pseudovarieties of Relational Morphisms

    1. John Rhodes, Benjamin Steinberg
      Pages 1-33
    2. John Rhodes, Benjamin Steinberg
      Pages 1-78
    3. John Rhodes, Benjamin Steinberg
      Pages 1-86
  4. Complexity in Finite Semigroup Theory

    1. Front Matter
      Pages 1-1
  5. Part II Complexity in Finite Semigroup Theory

    1. John Rhodes, Benjamin Steinberg
      Pages 1-172
    2. John Rhodes, Benjamin Steinberg
      Pages 1-38
  6. The Algebraic Lattice of Semigroup Pseudovarieties

    1. Front Matter
      Pages 1-1
  7. Part III The Algebraic Lattice of Semigroup Pseudovarieties

    1. John Rhodes, Benjamin Steinberg
      Pages 1-34
    2. John Rhodes, Benjamin Steinberg
      Pages 1-59
  8. Quantales, Idempotent Semirings, Matrix Algebras and the Triangular Product

    1. Front Matter
      Pages 1-1
  9. Part IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product

    1. John Rhodes, Benjamin Steinberg
      Pages 1-23
    2. John Rhodes, Benjamin Steinberg
      Pages 1-48
  10. Back Matter
    Pages 1-68

About this book

Introduction

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 graduate student to the researcher/practitioner – with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research.

Key features:

 * Develops q-theory, a new theory that provides a unifying approach to finite semigroup theory via quantization;

* Contains the only contemporary exposition of the complete theory of the complexity of finite semigroups;

* Introduces spectral theory into finite semigroup theory;

* Develops the theory of profinite semigroups from first principles, making connections with spectra of Boolean algebras of regular languages;

* Presents over 70 research problems, most new, and hundreds of exercises.

Additional features:

* For newcomers, an appendix on elementary finite semigroup theory;

* Extensive bibliography and index.

The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, and thereby updates and modernizes the literature of semigroup theory.

Keywords

Boolean algebra Group theory Lattice Matrix Matrix Theory algebra complexity

Authors and affiliations

  • John Rhodes
    • 1
  • Benjamin Steinberg
    • 2
  1. 1.Dept. MathematicsUniversity of CaliforniaBerkeleyU.S.A.
  2. 2.School of Mathematics & StatisticsCarleton UniversityOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/b104443
  • Copyright Information Springer Science+Business Media, LLC 2009
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-09780-0
  • Online ISBN 978-0-387-09781-7
  • Series Print ISSN 1439-7382