Published by De Gruyter 2011

Rings and Their Modules

Paul E. Bland

In the series De Gruyter Textbook

Overview
Contents

About this book

This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. The theme of the text is the interplay between rings and modules. At times rings are investigated by considering given sets of conditions on the modules they admit and at other times rings of a certain type are considered to see what structure is forced on their modules. Standard topics in ring and module theory such as chain conditions on rings and modules, injective and projective modules and semisimple rings are included as well as subjects like category theory and homological algebra. The text also contains presentations on topics such as flat modules and coherent rings, injective envelopes, projective covers and perfect rings, reflexive modules and quasi-Frobenius rings, and graded rings and modules.

The book is a self-contained volume written in a very systematic style: all proofs are clear and easy for the reader to understand and all arguments are based on materials contained in the book. A problem sets follow each section.

It is assumed that the reader is familiar with concepts such as Zorn's lemma, commutative diagrams and ordinal and cardinal numbers. It is also assumed that the reader has a basic knowledge of rings and their homomorphisms. The text is suitable for graduate and PhD students who have chosen ring theory for their research subject.

Suitable for graduate students and researchers
Includes lots of exercises with tips

Author / Editor information

Paul E. Bland, Eastern Kentucky University, USA.

Reviews

"This recent book is a welcome addition to the textbook literature on the subject of (mostly noncommutative) ring theory [...] The author of this text is clearly interested in making this material, and what follows, as accessible as possible to a graduate student. [...] This book has all the attributes of an excellent text. The writing is clear and reader-friendly, and there are both good examples and a reasonable number of exercises of varying difficulty. ... It is highly recommended, both as a text for ring theory courses at the various levels described above, or as an accessible resource for graduate students with an interest in pursuing research in ring theory."
Mark Hunacek, MAA Reviews

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Preface Requires Authentication Unlicensed Licensed Download PDF	V
Contents Requires Authentication Unlicensed Licensed Download PDF	IX
0 Preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
1 Basic Properties of Rings and Modules Requires Authentication Unlicensed Licensed Download PDF	7
2 Fundamental Constructions Requires Authentication Unlicensed Licensed Download PDF	39
3 Categories Requires Authentication Unlicensed Licensed Download PDF	71
4 Chain Conditions Requires Authentication Unlicensed Licensed Download PDF	104
5 Injective, Projective, and Flat Modules Requires Authentication Unlicensed Licensed Download PDF	135
6 Classical Ring Theory Requires Authentication Unlicensed Licensed Download PDF	171
7 Envelopes and Covers Requires Authentication Unlicensed Licensed Download PDF	216
8 Rings and Modules of Quotients Requires Authentication Unlicensed Licensed Download PDF	254
9 Graded Rings and Modules Requires Authentication Unlicensed Licensed Download PDF	294
10 More on Rings and Modules Requires Authentication Unlicensed Licensed Download PDF	331
11 Introduction to Homological Algebra Requires Authentication Unlicensed Licensed Download PDF	348
12 Homological Methods Requires Authentication Unlicensed Licensed Download PDF	395
A Ordinal and Cardinal Numbers Requires Authentication Unlicensed Licensed Download PDF	429
Bibliography Requires Authentication Unlicensed Licensed Download PDF	437
List of Symbols Requires Authentication Unlicensed Licensed Download PDF	441
Index Requires Authentication Unlicensed Licensed Download PDF	443

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Students, Researchers; Academic Libraries
Pages
- Front matter: 13
- Main content: 452
Keywords: Ring Theory; Module Theory; Homological Algebra

eBook

Published: February 1, 2011
ISBN: 9783110250237

Hardcover

Published: January 28, 2011
ISBN: 9783110250220