Dualisability

Unary Algebras and Beyond

  • Jane Pitkethly
  • Brian Davey

Part of the Advances in Mathematics book series (ADMA, volume 9)

About this book

Introduction

Natural duality theory is one of the major growth areas within general algebra. This text provides a short path to the forefront of research in duality theory. It presents a coherent approach to new results in the area, as well as exposing open problems.

Unary algebras play a special role throughout the text. Individual unary algebras are relatively simple and easy to work with. But as a class they have a rich and complex entanglement with dualisability. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples.

A number of results appear here for the first time. In particular, the text ends with an appendix that provides a new and definitive approach to the concept of the rank of a finite algebra and its relationship with strong dualisability.

 

Audience

This book is intended for established researchers in natural duality theory, general algebraists wishing to commence research in duality theory, and graduate students in algebra.

Keywords

Duality theory Finite General algebra Morphism Quasivarieties Topological representations Unary algebras algebra

Authors and affiliations

  • Jane Pitkethly
    • 1
  • Brian Davey
    • 1
  1. 1.La Trobe UniversityVictoriaAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-27570-3
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-27569-7
  • Online ISBN 978-0-387-27570-3
  • About this book