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Other titles in the Frontiers in Mathematics series:
Functional Identities (Frontiers in Mathematics)by Matej Bresar
Synopses & ReviewsPublisher Comments: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 dfree set; various constructions and concrete examples of dfree sets are given, and FI's on dfree 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 longstanding Herstein's conjectures on Lie homomorphisms and Lie derivations  in the proofs practically the entire FI theory is used.
Synopsis:A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The theory of functional identities is a relatively new one, and this is the first book on this subject. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory.
Synopsis:The theory of functional identities is a relatively new one  the first papers were published at the beginning of the 1990s, and this is the first book on this subject. A functional identity 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 theory is to describe these functions, or, when this is not possible, to describe the structure of the ring admitting the functional identity 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.
Table of ContentsPart I. An Introductory Course  What is a functional identity? Strong degree and FIdegree. Part II. The General Theory Constructing dfree sets FIs on dfree sets FIs in (semi) prime rings. Part III. Applications  Lie maps and related topics Linear Preserver Problems Further Applications to Lie Algebras Appendices Bibliography.
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Science and Mathematics » Mathematics » Algebra » Abstract Algebra


