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  3. A Guide to Groups, Rings, and Fields
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  • Publisher:
    Mathematical Association of America
    Publication date:
    05 April 2013
    30 November 2012
    ISBN:
    9781614442110
    9780883853559
    DOI:
    https://doi.org/10.5948/UPO9781614442110
    Dimensions:
    Weight & Pages:
    00kg,
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics, Algebra
    Series:
    Dolciani Mathematical Expositions
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Subjects:
Mathematics, Algebra
Series:
Dolciani Mathematical Expositions
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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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