A Guide to Groups, Rings, and Fields
Seiten
2013
Mathematical Association of America (Verlag)
978-0-88385-355-9 (ISBN)
Mathematical Association of America (Verlag)
978-0-88385-355-9 (ISBN)
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This book provides a comprehensive and insightful guide to the many algebraic structures that are used in some form by almost all mathematicians. The book begins with groups and rings, and progresses to more exotic topics. A source of valuable information for graduate students and a useful reference for researchers.
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.
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.
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.
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.
| Erscheint lt. Verlag | 14.3.2013 |
|---|---|
| Reihe/Serie | Dolciani Mathematical Expositions |
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 550 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-88385-355-8 / 0883853558 |
| ISBN-13 | 978-0-88385-355-9 / 9780883853559 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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