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25 Remote Warehouse Mathematics- Abstract Algebra

Functional Identities (Frontiers in Mathematics)

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Functional Identities (Frontiers in Mathematics) Cover

 

Synopses & Reviews

Publisher 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 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.

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 Contents

Part I. An Introductory Course - What is a functional identity?- Strong degree and FI-degree.- Part II. The General Theory- Constructing d-free sets- FIs on d-free sets- FIs in (semi-) prime rings.- Part III. Applications - Lie maps and related topics- Linear Preserver Problems- Further Applications to Lie Algebras- Appendices- Bibliography.

Product Details

ISBN:
9783764377953
Author:
Bresar, Matej
Publisher:
Birkhauser Basel
Author:
Chebotar, Mikhail A.
Author:
Breaar, Matej
Author:
Bre?ar, Matej
Author:
Martindale, Wallace S.
Author:
Martindale 3rd, Wallace S.
Author:
Brešar, Matej
Subject:
Algebras, linear
Subject:
Associative rings.
Subject:
Algebra - General
Subject:
Functional Analysis
Subject:
lie algebra
Subject:
functional identity
Subject:
Linear Algebra
Subject:
Operator theory
Subject:
ring theory
Subject:
Algebra
Subject:
Associative Rings and Algebras
Subject:
Functional Analysis <P>First monograph devoted to functional identities and accessible to a wider audience</P> <P>Touching a variety of mathematical areas such as ring theory, algebra and operator theory</P>
Subject:
Mathematics - Algebra
Subject:
Mathematics-Abstract Algebra
Copyright:
Edition Description:
Book
Series:
Frontiers in Mathematics
Publication Date:
20070731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
272
Dimensions:
240 x 170 mm 466 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Functional Identities (Frontiers in Mathematics) New Trade Paper
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Product details 272 pages Birkhauser Basel - English 9783764377953 Reviews:
"Synopsis" by , 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" by , 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.
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