Ebook: Topological Rings Satisfying Compactness Conditions
Author: Mihail Ursul (auth.)
- Tags: Associative Rings and Algebras, Algebraic Topology, Topological Groups Lie Groups, Group Theory and Generalizations, Non-associative Rings and Algebras
- Series: Mathematics and Its Applications 549
- Year: 2002
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts.
Content:
Front Matter....Pages i-ix
Elements of topological groups....Pages 1-82
Topological rings....Pages 83-309
Back Matter....Pages 311-327
Content:
Front Matter....Pages i-ix
Elements of topological groups....Pages 1-82
Topological rings....Pages 83-309
Back Matter....Pages 311-327
....