Algebra and Applications

Classical Finite Transformation Semigroups

An Introduction

Authors: Ganyushkin, Olexandr, Mazorchuk, Volodymyr

  • Covers transformation semigroups
  • Presents results from the former Soviet Union semigroup schools
  • Accessible coverage that includes many examples
  • Ideal as an introduction to transformation semigroups and abstract semigroups
  • Includes historical remarks and open questions for further research
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eBook $89.00
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  • ISBN 978-1-84800-281-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-84800-280-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-84996-768-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

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)


Table of contents (14 chapters)

  • Ordinary and Partial Transformations

    Ganyushkin, Olexandr (et al.)

    Pages 1-14

  • The Semigroups T n, PT n, and IS n

    Ganyushkin, Olexandr (et al.)

    Pages 15-38

  • Generating Systems

    Ganyushkin, Olexandr (et al.)

    Pages 39-43

  • Ideals and Green ' s Relations

    Ganyushkin, Olexandr (et al.)

    Pages 45-67

  • Subgroups and Subsemigroups

    Ganyushkin, Olexandr (et al.)

    Pages 69-89

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-84800-281-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-1-84800-280-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-84996-768-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Classical Finite Transformation Semigroups
Book Subtitle
An Introduction
Authors
Series Title
Algebra and Applications
Series Volume
9
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84800-281-4
DOI
10.1007/978-1-84800-281-4
Hardcover ISBN
978-1-84800-280-7
Softcover ISBN
978-1-84996-768-6
Series ISSN
1572-5553
Edition Number
1
Number of Pages
XII, 328
Number of Illustrations and Tables
4 b/w illustrations
Topics