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Frontiers in Mathematics

Functional Identities

Authors: Bre#ar, Matej, Chebotar, Mikhail A., Martindale, Wallace S.

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  • First monograph devoted to functional identities and accessible to a wider audience
  • Touching a variety of mathematical areas such as ring theory, algebra and operator theory
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About this book

The theory of functional identities (FIs) is a relatively new one - the first results were published at the beginning of the 1990s, and this is the first book on this subject. An FI can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The goal of the general FI theory is to describe these functions, or, when this is not possible, to describe the structure of the ring admitting the FI in question. This abstract theory has turned out to be a powerful tool for solving a variety of problems in ring theory, Lie algebras, Jordan algebras, linear algebra, and operator theory.

The book is divided into three parts. Part I is an introductory one. Part II is the core of the book. It gives a full account of the general FI theory, which is based on the concept of a d-free set; various constructions and concrete examples of d-free sets are given, and FI’s on d-free sets are thoroughly studied. Part III deals with applications. Its main purpose is to demonstrate how one can find FI’s when considering different problems, and then effectively use the general theory exposed in Part II. Perhaps the most illuminating example of the applicability are solutions of long-standing Herstein’s conjectures on Lie homomorphisms and Lie derivations - in the proofs practically the entire FI theory is used.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for Mexico
  • ISBN 978-3-7643-7796-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for Mexico
  • ISBN 978-3-7643-7795-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Functional Identities
Authors
Series Title
Frontiers in Mathematics
Copyright
2007
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7796-0
DOI
10.1007/978-3-7643-7796-0
Softcover ISBN
978-3-7643-7795-3
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XII, 272
Topics

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