Items related to Functional Identities (Frontiers in Mathematics)
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.
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From the Back Cover
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.
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- PublisherBirkhäuser
- Publication date2007
- ISBN 10 376437795X
- ISBN 13 9783764377953
- BindingPaperback
- LanguageEnglish
- Number of pages284
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Functional Identities
Published by
Springer, Basel, Birkhäuser Basel, Birkhäuser, 2007
ISBN 10: 376437795X
ISBN 13: 9783764377953
New
Taschenbuch
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A functional identity (FI) can be informally described as an identical relation involving(arbitrary)elementsinaringtogetherwith('unknown')functions;more precisely,elementsaremultipliedbyvaluesoffunctions.ThegoalofthegeneralFI theory is to determine the form of these functions, or, when this is not possible, to determine the structure of the ring admitting the FI in question. This theory has turnedouttobeapowerfultoolfor solvingavarietyofproblemsindi erentareas. It is not always easy to recognize that the problem in question can be interpreted through some FI; often this is the most intriguing part of the process. But once one succeeds in discovering an FI that ts into the general theory, this abstract theory then as a rule yields the desired conclusions at a high level of generality. Among classical algebraic concepts, the one of a polynomial identity (PI) seems to be, at least on the surface, the closest one to the concept of an FI. In fact, a PI is formally just a very special example of an FI (where functions are polynomials).However,the theoryof PI'shasquite di erent goalsthan the theory of FI's. One could say, especially from the point of view of applications, that the twotheoriesarecomplementaryto eachother.Under somenaturalrestrictions,PI theorydealswithringsthatareclosetoalgebrasoflowdimensions,whileFItheory gives de nitive answers in algebras of su ciently large or in nite dimensions. 272 pp. Englisch. Seller Inventory # 9783764377953
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Functional Identities
Published by
Springer, Basel, Birkhäuser Basel, Birkhäuser, 2007
ISBN 10: 376437795X
ISBN 13: 9783764377953
New
Taschenbuch
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - A functional identity (FI) can be informally described as an identical relation involving(arbitrary)elementsinaringtogetherwith('unknown')functions;more precisely,elementsaremultipliedbyvaluesoffunctions.ThegoalofthegeneralFI theory is to determine the form of these functions, or, when this is not possible, to determine the structure of the ring admitting the FI in question. This theory has turnedouttobeapowerfultoolfor solvingavarietyofproblemsindi erentareas. It is not always easy to recognize that the problem in question can be interpreted through some FI; often this is the most intriguing part of the process. But once one succeeds in discovering an FI that ts into the general theory, this abstract theory then as a rule yields the desired conclusions at a high level of generality. Among classical algebraic concepts, the one of a polynomial identity (PI) seems to be, at least on the surface, the closest one to the concept of an FI. In fact, a PI is formally just a very special example of an FI (where functions are polynomials).However,the theoryof PI'shasquite di erent goalsthan the theory of FI's. One could say, especially from the point of view of applications, that the twotheoriesarecomplementaryto eachother.Under somenaturalrestrictions,PI theorydealswithringsthatareclosetoalgebrasoflowdimensions,whi leFItheory gives de nitive answers in algebras of su ciently large or in nite dimensions. Seller Inventory # 9783764377953
Quantity: 2 available