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This book provides an introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It contains many exercises and historical comments.
List of contents
Ordinary and Partial Transformations.- The Semigroups T n, PT n, and IS n.- Generating Systems.- Ideals and Green ' s Relations.- Subgroups and Subsemigroups.- Other Relations on Semigroups.- Endomorphisms.- Nilpotent Subsemigroups.- Presentation.- Transitive Actions.- Linear Representations.- Cross-Sections.- Variants.- Order-Related Subsemigroups.
Summary
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 also to tutors and researchers.
Additional text
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)
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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)
