Blick ins Buch

Functional Identities

Matej Brešar, Mikhail A. Chebotar, Wallace S. Martindale (Autoren)

Buch | Softcover

XII, 272 Seiten

2007 | 2007
Springer Basel (Verlag)
978-3-7643-7795-3 (ISBN)

Lese- und Medienproben

Blick ins Buch (midvox)

Artikel merken

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.

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.

Erscheint lt. Verlag	21.6.2007
Reihe/Serie	Frontiers in Mathematics
Zusatzinfo	XII, 272 p.
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Gewicht	570 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Algebra • functional identity • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • Homomorphism • Lie algebra • linear algebra • operator theory • Ring Theory
ISBN-10	3-7643-7795-X / 376437795X
ISBN-13	978-3-7643-7795-3 / 9783764377953
Zustand	Neuware