Topological Rings

Volume 178

By: S. Warner

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Hardcover | 7 July 1993

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497 Pages

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25.4 x 17.78 x 3.18

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This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included.

The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.

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Preface
Topological Rings and Modules
Examples of topological rings
Topological modules, vector spaces, and algebras
Neighbourhoods of zero
Subrings, ideals, submodules, and subgroups
Quotients and projective limits of rings and modules
Metrizability and Completeness
Metrizable groups
Completions of commutative Haussdorf groups
Completions of topological rings and modules
Baire spaces
Summability
Continuity of inversion and adversion
Local Boundedness
Locally bounded modules and rings
Locally retrobounded division rings
Norms and absolute values
Finite-dimensional vector spaces
Topological division rings
Real Valuations
Real valuations and valuation rings
Discrete valuations
Extensions of real valuations
Complete Local Rings
Noetherian modules and rings
Cohen subrings and complete local rings
Complete discretely valued fields
Complete local Noetherian rings
Complete semilocal Noetherian rings
Primitive and Semisimple Rings
Primitive rings
The radical of a ring
Artinian modules and rings
Linear Compactness and Semisimplicity
Linearly compact rings and modules
Linearly compact semisimple rings
Strongly linearly compact modules
Locally linearly compact semisimple rings
Locally compact semisimple rings
Linear Compactness in Rings with Radical
Linear compactness in rings with radical
Lifting idempotents
Locally compact rings
The radical topology
Complete Local Noetherian Rings
The principal ideal theorem
Krull dimension and regular local rings
Complete regular local rings
The Japanese property
Locally Centrally Linearly Compact Rings
Complete discretely valued fields and division rings
Finite-dimensional algebras
Locally centrally linearly compact rings
Historical Notes
Topologies on commutative rings
Locally and linearly compact rings
Category, duality and existence theorems
Bibliography
Errata
Index of Names
Index of Symbols and Definitions
Table of Contents provided by Publisher. All Rights Reserved.

Topological Rings

Volume 178

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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