Classical Finite Transformation Semigroups

An Introduction

Nonfiction, Science & Nature, Mathematics, Combinatorics, Algebra
Cover of the book Classical Finite Transformation Semigroups by Volodymyr Mazorchuk, Olexandr Ganyushkin, Springer London
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Author: Volodymyr Mazorchuk, Olexandr Ganyushkin ISBN: 9781848002814
Publisher: Springer London Publication: December 10, 2008
Imprint: Springer Language: English
Author: Volodymyr Mazorchuk, Olexandr Ganyushkin
ISBN: 9781848002814
Publisher: Springer London
Publication: December 10, 2008
Imprint: Springer
Language: English

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.

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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.

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