Algebra-行业好书-社会科学-太极之巅书单号

书刊介绍

内容简介

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

作品目录

Cover 1
Title page 4
Contents 6
Introduction 18
Chapter I. Preliminaries: Set theory and categories 24
Chapter II. Groups, first encounter 64
Chapter III. Rings and modules 142
Chapter IV. Groups, second encounter 210
Chapter V. Irreducibility and factorization in integral domains 266
Chapter VI. Linear algebra 328
Chapter VII. Fields 408
Chapter VIII. Linear algebra, reprise 506
Chapter IX. Homological algebra 582
Index 722
Back Cover 738
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