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A Guide to Groups, Rings, and Fields

Part of Dolciani Mathematical Expositions

Author: Fernando Q. Gouvêa, Colby College, Maine

Date Published: March 2013
availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
format: Hardback
isbn: 9780883853559

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About the Authors

Algebraic structures have come to be ubiquitous in mathematics, with almost all mathematicians encountering groups, rings, fields or more exotic related objects during the course of their research. This book presents an overview of some of the most important algebraic structures in modern mathematics, with an emphasis on creating a coherent picture of how they all interact. In addition to the standard material on groups, rings, modules, fields and Galois theory, the book includes discussions of other important topics, including linear groups, group representations, Artinian rings, projective, injective and flat modules, Dedekind domains and central simple algebras. All of the important theorems are discussed, typically without proofs, but often with a discussion of the intuitive ideas behind those proofs. This insightful guide is ideal for both graduate students in mathematics who are beginning their studies, and researchers who wish to understand the bigger picture of the algebraic structures they encounter.
- A handy reference guide for mathematicians, particularly those who wish to refresh their basic algebra
- The guide demonstrates the big picture of how different areas of the theory fit together
- Emphasises aspects of the theory that are useful in other areas of mathematics
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Product details
- Date Published: March 2013
- format: Hardback
- isbn: 9780883853559
- length: 326 pages
- dimensions: 235 x 155 x 22 mm
- weight: 0.55kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
Preface
A guide to this guide
1. Algebra: classical, modern, and ultramodern
2. Categories
3. Algebraic structures
4. Groups and their representations
5. Rings and modules
6. Fields and skew fields
Bibliography
Index of notations
Index.

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Author
Fernando Q. Gouvêa, Colby College, Maine
Fernando Q. Gouvêa is the Carter Professor of Mathematics at Colby College, Maine. He was editor of MAA Focus, the newsletter of the Mathematical Association of America, from 1999 to 2010 and is currently editor of MAA Reviews and the Carus Mathematical Monographs book series. He has written several books, including Math Through the Ages, with William P. Berlinghoff, which was awarded the 2007 Beckenbach Book Prize.