Algebra: Chapter 0

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.
Algebra: Chapter 0是对代数主要主题的独立介绍，适合在初级研究生或本科高年级阶段对该主题进行第一序列。与标准代数教科书相比，本书的主要区别在于早期引入了类别，在主要主题的呈现中用作统一主题。第二个特点是强调同调代数：一旦引入模块，就会介绍复数的基本概念，而关于同调代数的广泛最后一章可以构成该主题的后续入门课程的基础。大约 1,000 个练习既提供了足够的练习来巩固对文本主体的理解，也提供了探索许多其他主题的机会，包括数论和代数几何的应用。这将使教师能够根据他们的特定主题选择调整教科书，并为独立读者提供更丰富的代数机会。许多练习都包含大量提示，广泛的索引和数百个交叉引用有助于主题的导航。