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Mathematics - Algebra | Classical Finite Transformation Semigroups - An Introduction

Classical Finite Transformation Semigroups

An Introduction

Series: Algebra and Applications, Vol. 9

Ganyushkin, Olexandr, Mazorchuk, Volodymyr

2009

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  • 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

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.

Content Level » Research

Keywords » Cardinality - Idempotent - Semigroups - Transformations

Related subjects » Algebra

Table 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.

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