Topological Rings

Hardcover (Print)
Buy New
Buy New from BN.com
$72.95
Used and New from Other Sellers
Used and New from Other Sellers
from $220.49
Usually ships in 1-2 business days
Other sellers (Hardcover)
  • All (1) from $220.49   
  • New (1) from $220.49   

Overview

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.

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

Read More Show Less

Product Details

Table of Contents

Preface
Ch. I Topological Rings and Modules 1
1 Examples of Topological Rings 1
2 Topological Modules, Vector Spaces, and Algebras 11
3 Neighborhoods of Zero 18
4 Subrings, Ideals, Submodules, and Subgroups 23
5 Quotients and Projective Limits of Rings and Modules 32
Ch. II Metrizability and Completeness 44
6 Metrizable Groups 44
7 Completions of Commutative Hausdorff Groups 55
8 Completions of Topological Rings and Modules 64
9 Baire Spaces 68
10 Summability 71
11 Continuity of Inversion and Adversion 80
Ch. III Local Boundedness 88
12 Locally Bounded Modules and Rings 88
13 Locally Retrobounded Division Rings 94
14 Norms and Absolute Values 102
15 Finite-dimensional Vector Spaces 112
16 Topological Division Rings 120
Ch. IV Real Valuations 134
17 Real Valuations and Valuation Rings 134
18 Discrete Valuations 141
19 Extensions of Real Valuations 152
Ch. V Complete Local Rings 166
20 Noetherian Modules and Rings 166
21 Cohen Subrings of Complete Local Rings 173
22 Complete Discretely Valued Fields 186
23 Complete Local Noetherian Rings 192
24 Complete Semilocal Noetherian Rings 197
Ch. VI Primitive and Semisimple Rings 206
25 Primitive Rings 206
26 The Radical of a Ring 216
27 Artinian Modules and Rings 226
Ch. VII Linear Compactness and Semisimplicity 232
28 Linearly Compact Rings and Modules 232
29 Linearly Compact Semisimple Rings 241
30 Strongly Linearly Compact Modules 251
31 Locally Linearly Compact Semisimple Rings 256
32 Locally Compact Semisimple Rings 267
Ch. VIII Linear Compactness in Rings with Radical 283
33 Linear Compactness in Rings with Radical 283
34 Lifting Idempotents 295
35 Locally Compact Rings 317
36 The Radical Topology 330
Ch. IX Complete Local Noetherian Rings 359
37 The Principal Ideal Theorem 359
38 Krull Dimension and Regular Local Rings 368
39 Complete Regular Local Rings 377
40 The Japanese Property 391
Ch. X Locally Centrally Linearly Compact Rings 398
41 Complete Discretely Valued Fields and Division Rings 398
42 Finite-dimensional Algebras 406
43 Locally Centrally Linearly Compact Rings 414
Ch. XI Historical Notes 424
44 Topologies on Commutative Rings 424
45 Locally and Linearly Compact Rings 428
46 Category, Duality, and Existence Theorems 435
Bibliography 440
Errata 487
Index of Names 489
Index of Symbols and Definitions 492
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)