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Homological methods in commutative algebra / Andrea Ferretti

By: Resource type: Ressourcentyp: BuchBookLanguage: English Series: Graduate studies in mathematics ; 234Publisher: Providence, Rhode Island : American Mathematical Society, [2023]Copyright date: © 2023Description: xviii, 411 Seiten : IllustrationenISBN:
  • 9781470471286
  • 9781470474362
Subject(s): Additional physical formats: 9781470474355. | Erscheint auch als: Homological methods in commutative algebra. Online-Ausgabe Providence, Rhode Island : American Mathematical Society, 2023. 1 Online-Ressource (xviii, 411 Seiten) | Erscheint auch als: Homological methods in commutative algebra. Online-Ausgabe Providence, Rhode Island : American Mathematical Society, 2023. 1 Online-Ressource (xviii, 411 Seiten)DDC classification:
  • 512/.44 23/eng20230711
MSC: MSC: 13-01 | 13D02 | 13D07 | 13D45 | 13H10LOC classification:
  • QA251.3
Summary: This book develops the machinery of homological algebra and its applications to commutative rings and modules. It assumes familiarity with basic commutative algebra, for example, as covered in the author’s book, Commutative Algebra (Graduate Studies in Mathematics, Volume 233). The first part of the book is an elementary but thorough exposition of the concepts of homological algebra, starting from categorical language up to the construction of derived functors and spectral sequences. A full proof of the celebrated Freyd-Mitchell theorem on the embeddings of small Abelian categories is included. The second part of the book is devoted to the application of these techniques in commutative algebra through the study of projective, injective, and flat modules, the construction of explicit resolutions via the Koszul complex, and the properties of regular sequences. The theory is then used to understand the properties of regular rings, Cohen-Macaulay rings and modules, Gorenstein rings and complete intersections. Overall, this book is a valuable resource for anyone interested in learning about homological algebra and its applications in commutative algebra. The clear and thorough presentation of the material, along with the many examples and exercises of varying difficulty, make it an excellent choice for self-study or as a reference for researchers.PPN: PPN: 185298581X
Holdings
Item type Home library Shelving location Call number Status Date due Barcode Item holds
Freihandbestand ausleihbar Fachbibliothek Mathematik Bibliothek / frei aufgestellt Algebr. / Fer Available 36530565090
Total holds: 0
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