Hardcover ISBN:  9780883853559 
Product Code:  DOL/48 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614442110 
Product Code:  DOL/48.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853559 
eBook: ISBN:  9781614442110 
Product Code:  DOL/48.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 
Hardcover ISBN:  9780883853559 
Product Code:  DOL/48 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614442110 
Product Code:  DOL/48.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853559 
eBook ISBN:  9781614442110 
Product Code:  DOL/48.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 48; 2012; 309 pp
This book offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs.
Those looking for a way to review and refresh their basic algebra will benefit from reading this guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.

Table of Contents

Chapters

A Guide to this Guide

Chapter 1. Algebra: Classical, Modern, and Ultramodern

Chapter 2. Categories

Chapter 3. Algebraic Structures

Chapter 4. Groups and their Representations

Chapter 5. Rings and Modules

Chapter 6. Fields and Skew Fields


Additional Material

Reviews

... Billed as delivering a concise, graduatelevel overview of the theory of groups, rings, and fields, it emphasizes the main ideas and how they hang together, as well as the ways these subjects are used in other parts of mathematics. ... Overall, an enjoyable volume.
F.E.J. Linton, CHOICE 
This expository algebra book is highly unusual—but in a very successful manner.
Tom De Medts, Mathematical Reviews 
This book is one of the latest in the MAA series of guides to different areas of mathematics intended to summarize the material graduate students need to know in preparing for PhD comprehensive exams. This one in particular, is welcome since the area, abstract algebra is a required exam subject at many universities. The organization of the book is straightforward with three brief introductory chapters (totalling 28 pages) giving a bit of history, a very little bit of category theory, and some observations on the organization of the subject. ... number theorists, operator theorists, and students in most other areas will find this book most satisfactory in all respects.
CMS Notes


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This book offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs.
Those looking for a way to review and refresh their basic algebra will benefit from reading this guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.

Chapters

A Guide to this Guide

Chapter 1. Algebra: Classical, Modern, and Ultramodern

Chapter 2. Categories

Chapter 3. Algebraic Structures

Chapter 4. Groups and their Representations

Chapter 5. Rings and Modules

Chapter 6. Fields and Skew Fields

... Billed as delivering a concise, graduatelevel overview of the theory of groups, rings, and fields, it emphasizes the main ideas and how they hang together, as well as the ways these subjects are used in other parts of mathematics. ... Overall, an enjoyable volume.
F.E.J. Linton, CHOICE 
This expository algebra book is highly unusual—but in a very successful manner.
Tom De Medts, Mathematical Reviews 
This book is one of the latest in the MAA series of guides to different areas of mathematics intended to summarize the material graduate students need to know in preparing for PhD comprehensive exams. This one in particular, is welcome since the area, abstract algebra is a required exam subject at many universities. The organization of the book is straightforward with three brief introductory chapters (totalling 28 pages) giving a bit of history, a very little bit of category theory, and some observations on the organization of the subject. ... number theorists, operator theorists, and students in most other areas will find this book most satisfactory in all respects.
CMS Notes