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Commutative Algebra
 
Softcover ISBN:  978-1-4704-7434-8
Product Code:  GSM/233.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7433-1
Product Code:  GSM/233.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7434-8
eBook: ISBN:  978-1-4704-7433-1
Product Code:  GSM/233.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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Commutative Algebra
Softcover ISBN:  978-1-4704-7434-8
Product Code:  GSM/233.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7433-1
Product Code:  GSM/233.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7434-8
eBook ISBN:  978-1-4704-7433-1
Product Code:  GSM/233.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: 2332023; 373 pp
    MSC: Primary 13; 11; 14

    This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra.

    The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra (Graduate Studies in Mathematics, Volume 234).

    Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.

    Readership

    Graduate students and researchers interested in commutative algebra.

  • Table of Contents
     
     
    • Chapters
    • Basics
    • Finiteness conditions
    • Factorization
    • Computational methods
    • Integral dependence
    • Lattice methods
    • Metric and topological methods
    • Geometric dictionary
    • Dimension theory
    • Local structure
    • Fields
  • Reviews
     
     
    • In my opinion, [this volume] is an excellent choice for a one-semester introductory course on commutative algebra.

      Pramod Achar, Notices of the AMS
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 2332023; 373 pp
MSC: Primary 13; 11; 14

This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from a geometric perspective, providing further insight and motivation for the study of commutative algebra.

The content covers the classical theory of Noetherian rings, including primary decomposition and dimension theory, topological methods such as completions, computational techniques, local methods and multiplicity theory, as well as some topics of a more arithmetic nature, including the theory of Dedekind rings, lattice embeddings, and Witt vectors. Homological methods appear in the author's sequel, Homological Methods in Commutative Algebra (Graduate Studies in Mathematics, Volume 234).

Overall, this book is an excellent resource for advanced undergraduates and beginning graduate students in algebra or number theory. It is also suitable for students in neighboring fields such as algebraic geometry who wish to develop a strong foundation in commutative algebra. Some parts of the book may be useful to supplement undergraduate courses in number theory, computational algebra or algebraic geometry. The clear and detailed presentation, the inclusion of computational techniques and arithmetic topics, and the numerous exercises make it a valuable addition to any library.

Readership

Graduate students and researchers interested in commutative algebra.

  • Chapters
  • Basics
  • Finiteness conditions
  • Factorization
  • Computational methods
  • Integral dependence
  • Lattice methods
  • Metric and topological methods
  • Geometric dictionary
  • Dimension theory
  • Local structure
  • Fields
  • In my opinion, [this volume] is an excellent choice for a one-semester introductory course on commutative algebra.

    Pramod Achar, Notices of the AMS
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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