Algebra : chapter 0
Author(s)
Bibliographic Information
Algebra : chapter 0
（Graduate studies in mathematics, v. 104）
American Mathematical Society, c2009
Available at / 45 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
ALU||1||1200010707404
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Note
Includes index
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Chapter I. Preliminaries: Set theory and categories
Chapter II. Groups, first encounter
Chapter III. Rings and modules
Chapter IV. Groups, second encounter
Chapter V. Irreducibility and factorization in integral domains
Chapter VI. Linear algebra
Chapter VII. Fields
Chapter VIII. Linear algebra, reprise
Chapter IX. Homological algebra
Index
by "Nielsen BookData"