Includes bibliographical references (pages 277-282) and index.
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.
(source: Nielsen Book Data)
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. (source: Nielsen Book Data)