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Homological Methods in Commutative Algebra
 
Softcover ISBN:  978-1-4704-7436-2
Product Code:  GSM/234.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7435-5
Product Code:  GSM/234.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7436-2
eBook: ISBN:  978-1-4704-7435-5
Product Code:  GSM/234.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
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Homological Methods in Commutative Algebra
Softcover ISBN:  978-1-4704-7436-2
Product Code:  GSM/234.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7435-5
Product Code:  GSM/234.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7436-2
eBook ISBN:  978-1-4704-7435-5
Product Code:  GSM/234.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2342023; 411 pp
    MSC: Primary 13

    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.

    Readership

    Graduate students and researchers interested in commutative algebra.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Reviews
     
     
    • This two-volume set [see Volume 1, GSM/233] provides an engaging and friendly introduction to the subject and is a welcome addition to the literature.

      Pramod Achar, Notices of the AMS
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2342023; 411 pp
MSC: Primary 13

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.

Readership

Graduate students and researchers interested in commutative algebra.

  • Chapters
  • 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
  • This two-volume set [see Volume 1, GSM/233] provides an engaging and friendly introduction to the subject and is a welcome addition to the literature.

    Pramod Achar, Notices of the AMS
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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