Classical Finite Transformation Semigroups

An Introduction
1. Auflage. 2008
ISBN: 978-1-84800-280-7
Verlag: Springer

Buch, Englisch, Band 9, 328 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 658 g

Reihe: Algebra and Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Mazorchuk, Volodymyr

Ganyushkin, Olexandr

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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.