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  1. Home
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  3. A Guide to Groups, Rings, and Fields
  • This book is no longer available to purchase from Cambridge Core
  • Cited by 3
Publisher:
Mathematical Association of America
Online publication date:
April 2013
Print publication year:
2012
Online ISBN:
9781614442110
DOI:
https://doi.org/10.5948/UPO9781614442110
Subjects:
Mathematics, Algebra
Series:
Dolciani Mathematical Expositions
Information

Book description

This Guide 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.

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