Topological Rings Satisfying Compactness Conditions

  • Mihail Ursul

Part of the Mathematics and Its Applications book series (MAIA, volume 549)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Mihail Ursul
    Pages 1-82
  3. Mihail Ursul
    Pages 83-309
  4. Back Matter
    Pages 311-327

About this book

Introduction

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.

Keywords

Abelian group algebra topological group

Authors and affiliations

  • Mihail Ursul
    • 1
  1. 1.Universitatea Din OradeaOradeaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-0249-3
  • Copyright Information Kluwer Academic Publishers 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-3946-8
  • Online ISBN 978-94-010-0249-3
  • About this book