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Hardcover ISBN:  9781470471286 
Product Code:  GSM/234 
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AMS Member Price:  $108.00 
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Softcover ISBN:  9781470474362 
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eBook ISBN:  9781470474355 
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Hardcover ISBN:  9781470471286 
eBook ISBN:  9781470474355 
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MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Sale Price:  $143.00 $115.38 
Softcover ISBN:  9781470474362 
eBook ISBN:  9781470474355 
Product Code:  GSM/234.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
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Book DetailsGraduate Studies in MathematicsVolume: 234; 2023; 411 ppMSC: 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 FreydMitchell 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, CohenMacaulay 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 selfstudy or as a reference for researchers.
ReadershipGraduate 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


Additional Material

Reviews

This twovolume 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


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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 FreydMitchell 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, CohenMacaulay 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 selfstudy or as a reference for researchers.
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 twovolume 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