Homological Methods in Commutative Algebra
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Homological Methods in Commutative Algebra

Homological Methods in Commutative Algebra

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About the Book

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. 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.

Table of Contents:
Categories Abelian categories Derived functors Spectral sequences Projective and injective modules Flatness Koszul complexes and regular sequences Regularity Mild singularities Local cohomology and duality Background material Bibliography Index of notation Index


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Product Details
  • ISBN-13: 9781470471286
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 254 mm
  • No of Pages: 413
  • Width: 178 mm
  • ISBN-10: 1470471280
  • Publisher Date: 31 Jan 2024
  • Binding: Hardback
  • Language: English
  • Weight: 367 gr


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