A guide to groups, rings, and fields /

A guide to groups, rings, and fields /

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Bibliographic Details
Author / Creator:	Gouvêa, Fernando Q. (Fernando Quadros), author.
Imprint:	Washington, DC : Mathematical Association of America, 2012.
Description:	1 online resource (xvii, 309 pages)
Language:	English
Series:	Dolciani mathematical expositions ; #48 MAA guides ; #8 Dolciani mathematical expositions ; no. 48. MAA guides ; no. 8.
Subject:	Algebra. Rings (Algebra) Algebraic fields. Algebra. Algebraic fields. Rings (Algebra) Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11169392

Hidden Bibliographic Details
ISBN:	9781614442110 1614442118 0883853558 9780883853559
Notes:	Includes bibliographical references and index. Print version record.
Summary:	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.
Other form:	Print version: Gouvea, Fernando Q. Guide to groups, rings, and fields. Washington : Mathematical Assn America, 2012 0883853558

Table of Contents:

Algebra : classical, modern, and ultramodern ; Categories ; Algebraic structures ; Groups and their representations ; Rings and modules ; Fields and skew fields.