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## Details

Genre/Form: | Electronic books Textbooks |
---|---|

Additional Physical Format: | Print version: Aluffi, Paolo, 1960- Algebra : chapter 0. Providence, Rhode Island : American Mathematical Society, ©2009 xix, 713 pages |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Paolo Aluffi |

ISBN: | 9781470411688 1470411687 |

OCLC Number: | 908071072 |

Notes: | Includes index. |

Description: | 1 online resource (739 pages) : illustrations. |

Contents: | Preliminaries: set theory and categories -- Groups, first encounter -- Rings and modules -- Groups, second encounter -- Irreducibility and factorization in integral domains -- Linear algebra -- Fields -- Linear algebra, reprise -- Homological algebra. |

Series Title: | Graduate studies in mathematics, v. 104. |

Responsibility: | Paolo Aluffi. |

### Abstract:

"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."--Jacket.

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