**Graduate Studies in Mathematics**

Volume: 104;
2009;
713 pp;
Hardcover

MSC: Primary 00;
Secondary 12; 13; 15; 18; 20

Print ISBN: 978-0-8218-4781-7

Product Code: GSM/104

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-1168-8
Product Code: GSM/104.E**

List Price: $89.00

Individual Member Price: $71.20

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#### Supplemental Materials

# Algebra: Chapter 0

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*Paolo Aluffi*

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.

#### Readership

Undergraduate and graduate students interested in algebra.

#### Reviews & Endorsements

An obvious question: why another graduate algebra book? Aren't there all but too many already? Is there anything genuinely novel to be done when it comes to educating fledgling graduate students in this subject, given such an already well-populated and high-quality field? Well, the answer is yes. And the title of the book under review, Algebra: Chapter 0, is already a clue to what the author, Paolo Aluffi, is up to. In a perhaps Bourbakian sense, the prevailing motivation and objective is to present the subject at hand in a manner that pays proper due to relatively new foundations, making for a rather different orientation and flavor for what ensues. ...His treatment of these preliminaries is thorough as well as eminently accessible: Aluffi writes well, clearly and engagingly. This characterizes all of Algebra: Chapter 0, actually, and makes it easy to recommend the book enthusiastically even aside from the fact that I am a big fan of category theory to begin with.

-- MAA Online

This self-contained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme.

-- SciTech Book News

#### Table of Contents

# Table of Contents

## Algebra: Chapter 0

- Cover Cover11
- Title page iii4
- Contents v6
- Introduction xvii18
- Chapter I. Preliminaries: Set theory and categories 324
- Chapter II. Groups, first encounter 4364
- Chapter III. Rings and modules 121142
- Chapter IV. Groups, second encounter 189210
- Chapter V. Irreducibility and factorization in integral domains 245266
- Chapter VI. Linear algebra 307328
- Chapter VII. Fields 387408
- Chapter VIII. Linear algebra, reprise 485506
- Chapter IX. Homological algebra 561582
- Index 701722
- Back Cover Back Cover1738