Overview
- Using pictorial unary algebras as a source of examples, this text takes a reader with a minimal background in general algebra to the forefront of research in natural duality theory
Part of the book series: Advances in Mathematics (ADMA, volume 9)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews of the first edition:
"This fascinating book shows that even in the realm of unary algebras, where one might expect the situation to be virtually trivial almost all pathological behaviour occurs already. … The list of references is thorough and the index excellent." (Sheila Oates-Williams, Zentralblatt MATH, Vol. 1085, 2006)
Authors and Affiliations
Bibliographic Information
Book Title: Dualisability
Book Subtitle: Unary Algebras and Beyond
Authors: Jane Pitkethly, Brian Davey
Series Title: Advances in Mathematics
DOI: https://doi.org/10.1007/0-387-27570-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2005
Hardcover ISBN: 978-0-387-27569-7Published: 29 July 2005
Softcover ISBN: 978-1-4419-3901-2Published: 08 December 2010
eBook ISBN: 978-0-387-27570-3Published: 30 March 2006
Edition Number: 1
Number of Pages: XII, 264
Number of Illustrations: 38 b/w illustrations
Topics: General Algebraic Systems, Combinatorics, Order, Lattices, Ordered Algebraic Structures, Science, Humanities and Social Sciences, multidisciplinary