Functional Identities / by Matej Brešar, Mikhail A. Chebotar, Wallace S. Martindale
(Frontiers in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Birkhäuser Basel |
| 出版年 | 2007 |
| 本文言語 | 英語 |
| 大きさ | XII, 272 p : online resource |
書誌詳細を非表示
| 内容注記 | An Introductory Course What is a Functional Identity? The Strong Degree and the FI-Degree The General Theory Constructing d-Free Sets Functional Identities on d-Free Sets Functional Identities in (Semi)prime Rings Applications Lie Maps and Related Topics Linear Preserver Problems Further Applications to Lie Algebras |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Brešar, Matej author Chebotar, Mikhail A. author Martindale, Wallace S. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebra LCSH:Associative rings LCSH:Rings (Algebra) LCSH:Functional analysis FREE:Mathematics FREE:Algebra FREE:Associative Rings and Algebras FREE:Functional Analysis |
| 分 類 | DC23:512 |
| 巻冊次 | ISBN:9783764377960 
|
| ISBN | 9783764377960 |
| URL | http://dx.doi.org/10.1007/978-3-7643-7796-0 |
目次／あらすじ