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.
Author(s): Seth Warner (Eds.)
Series: North-Holland Mathematics Studies 178
Edition: 1
Publisher: Elsevier, Academic Press
Year: 1993
Language: English
Pages: iii-viii, 1-498
Content:
Edited by
Page iii
Copyright page
Page iv
Preface
Pages vii-viii
Chapter I Topological Rings and Modules
Pages 1-43
Chapter II Metrizability and Completeness
Pages 44-87
Chapter III Local Boundedness
Pages 88-133
Chapter IV Real Valuations
Pages 134-165
Chapter V Complete Local Rings
Pages 166-205
Chapter VI Primitive and Semisimple Rings
Pages 206-231
Chapter VII Linear Compactness and Semisimplicity
Pages 232-282
Chapter VIII Linear Compactness in Rings with Radical
Pages 283-358
Chapter IX Complete Local Noethekjan Rings
Pages 359-397
Chapter X Locally Centrally Linearly Compact Rings
Pages 398-423
Chapter XI Historical Notes
Pages 424-439
Bibliography
Pages 440-486
Errata
Pages 487-488
Index of Names
Pages 489-491
Index of Symbols and Definitions
Pages 492-498
