| 书目名称 | Functional Identities | | 编辑 | Matej Brešar,Mikhail A. Chebotar,Wallace S. Martin | | 视频video | http://file.papertrans.cn/350/349700/349700.mp4 | | 概述 | First monograph devoted to functional identities and accessible to a wider audience.Touching a variety of mathematical areas such as ring theory, algebra and operator theory.Includes supplementary mat | | 丛书名称 | Frontiers in Mathematics | | 图书封面 |  | | 描述 | 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 twothe | | 出版日期 | Book 2007 | | 关键词 | Lie algebra; Operator theory; algebra; functional identity; homomorphism; linear algebra; ring theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-7643-7796-0 | | isbn_softcover | 978-3-7643-7795-3 | | isbn_ebook | 978-3-7643-7796-0Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | Birkh�user Basel 2007 |
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