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.
- 432 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Homological Methods in Commutative Algebra
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- Cover
- Title page
- Contents
- Preface
- Chapter 1. Categories
- Chapter 2. Abelian Categories
- Chapter 3. Derived Functors
- Chapter 4. Spectral Sequences
- Chapter 5. Projective and Injective Modules
- Chapter 6. Flatness
- Chapter 7. Koszul Complexes and Regular Sequences
- Chapter 8. Regularity
- Chapter 9. Mild Singularities
- Chapter 10. Local Cohomology and Duality
- Appendix A. Background Material
- Bibliography
- Index of Notation
- Index
- Back Cover
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Yes, you can access Homological Methods in Commutative Algebra by Andrea Ferretti in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.