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© 2009

Classical Finite Transformation Semigroups

An Introduction

  • First book about transformation semigroups

  • First book presenting results from former Soviet Union semigroup schools

  • Easy to read, although fully detailed with many examples

  • Can be used both as an introduction to transformation semigroups and abstract semigroups

  • Has many historical remarks and open questions for further research

Book

Part of the Algebra and Applications book series (AA, volume 9)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 1-14
  3. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 15-38
  4. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 39-43
  5. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 45-67
  6. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 69-89
  7. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 91-110
  8. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 111-129
  9. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 131-152
  10. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 153-174
  11. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 175-188
  12. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 189-213
  13. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 215-236
  14. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 237-250
  15. Olexandr Ganyushkin, Volodymyr Mazorchuk
    Pages 251-275
  16. Back Matter
    Pages 277-314

About this book

Introduction

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers.

Keywords

Cardinality DEX Finite Idempotent Morphism Semigroups Transformations congruence form presentation semigroup sets transformation

Authors and affiliations

  1. 1.Kyiv Taras Shevchenko UniversityKyivUkraine
  2. 2.Dept. MathematicsUppsala UniversityUppsalaSweden

Bibliographic information

  • Book Title Classical Finite Transformation Semigroups
  • Book Subtitle An Introduction
  • Authors Olexandr Ganyushkin
    Volodymyr Mazorchuk
  • Series Title Algebra and Applications
  • DOI https://doi.org/10.1007/978-1-84800-281-4
  • Copyright Information Springer-Verlag London 2009
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-84800-280-7
  • Softcover ISBN 978-1-84996-768-6
  • eBook ISBN 978-1-84800-281-4
  • Series ISSN 1572-5553
  • Series E-ISSN 2192-2950
  • Edition Number 1
  • Number of Pages XII, 328
  • Number of Illustrations 4 b/w illustrations, 0 illustrations in colour
  • Topics Group Theory and Generalizations
    Combinatorics
  • Buy this book on publisher's site

Reviews

From the reviews:

"The book is self-contained and so accessible to university students. … the book will be an excellent source of ideas for graduate students in transformation semigroups as it lays out a pattern of research topics for the reader to consider. … The book is rich in exercises; the topic lends to it, and there are hints and answers where appropriate. There is also a good bibliography and notation list … overall the text is up-to-date and does a thorough job." (P. M. Higgins, Mathematical Reviews, Issue 2009 i)

“The reader is introduced to the basics of abstract semigroup theory. … at the end of each chapter a section with additional problems appears, some of which are easy exercises while others are more advanced (solutions of them are given in an appendix). The book is primarily directed to students who make their first steps in semigroup theory … .” (H. Mitsch, Monatshefte für Mathematik, Vol. 159 (4), March, 2010)