| Softcover ISBN: | 978-1-4704-6642-8 |
| Product Code: | SURV/259 |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-1-4704-6733-3 |
| Product Code: | SURV/259.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-6642-8 |
| eBook: ISBN: | 978-1-4704-6733-3 |
| Product Code: | SURV/259.B |
| List Price: | $250.00 $187.50 |
| MAA Member Price: | $225.00 $168.75 |
| AMS Member Price: | $200.00 $150.00 |
| Softcover ISBN: | 978-1-4704-6642-8 |
| Product Code: | SURV/259 |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-1-4704-6733-3 |
| Product Code: | SURV/259.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-6642-8 |
| eBook ISBN: | 978-1-4704-6733-3 |
| Product Code: | SURV/259.B |
| List Price: | $250.00 $187.50 |
| MAA Member Price: | $225.00 $168.75 |
| AMS Member Price: | $200.00 $150.00 |
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Book DetailsMathematical Surveys and MonographsVolume: 259; 2021; 426 ppMSC: Primary 13
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
ReadershipGraduate students and researchers interested in commutative algebra.
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Table of Contents
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Chapters
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Introduction
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Tools
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More tools
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First examples of the construction
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The Inclusion Construction
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Flatness and the Noetherian property
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The flat locus of an extension of polynomial rings
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Excellent rings and formal fibers
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Height-one prime ideals and weak flatness
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Insider Construction details
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Integral closure under extension to the completion
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Iterative examples
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Approximating discrete valuation rings by regular local rings
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Non-Noetherian examples of dimension 3
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Noetherian properties of non-Noetherian rings
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Non-Noetherian examples in higher dimension
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The Homomorphic Image Construction
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Catenary local rings with geometrically normal fibers
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An Ogoma-like example
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Multi-ideal-adic completions of Noetherian rings
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Noetherian flatness and multi-adic constructions
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Idealwise algebraic independence
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Idealwise algebraic independence II
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Krull domains with Noetherian $x$-adic completions
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Inclusion Constructions over excellent normal local domains
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Wierstrass techniques for generic fiber rings
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Generic fiber rings of mixed polynomial-power series rings
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Mixed polynomial-power series rings and relations among their spectra
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Extensions of local domains with trivial generic fiber
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Constructions and examples discussed in this book
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Additional Material
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Reviews
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In summary, this is, in my opinion, an excellent and impressive book: it is very well written, it covers a number of relevant and interesting topics in commutative ring theory, it presents many significant exercises and it can be very helpful both for researchers in the field and for students who seriously want to learn topics in this circle of ideas.
Carmelo Antonio Finocchiaro, University of Catania
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Graduate students and researchers interested in commutative algebra.
-
Chapters
-
Introduction
-
Tools
-
More tools
-
First examples of the construction
-
The Inclusion Construction
-
Flatness and the Noetherian property
-
The flat locus of an extension of polynomial rings
-
Excellent rings and formal fibers
-
Height-one prime ideals and weak flatness
-
Insider Construction details
-
Integral closure under extension to the completion
-
Iterative examples
-
Approximating discrete valuation rings by regular local rings
-
Non-Noetherian examples of dimension 3
-
Noetherian properties of non-Noetherian rings
-
Non-Noetherian examples in higher dimension
-
The Homomorphic Image Construction
-
Catenary local rings with geometrically normal fibers
-
An Ogoma-like example
-
Multi-ideal-adic completions of Noetherian rings
-
Noetherian flatness and multi-adic constructions
-
Idealwise algebraic independence
-
Idealwise algebraic independence II
-
Krull domains with Noetherian $x$-adic completions
-
Inclusion Constructions over excellent normal local domains
-
Wierstrass techniques for generic fiber rings
-
Generic fiber rings of mixed polynomial-power series rings
-
Mixed polynomial-power series rings and relations among their spectra
-
Extensions of local domains with trivial generic fiber
-
Constructions and examples discussed in this book
-
In summary, this is, in my opinion, an excellent and impressive book: it is very well written, it covers a number of relevant and interesting topics in commutative ring theory, it presents many significant exercises and it can be very helpful both for researchers in the field and for students who seriously want to learn topics in this circle of ideas.
Carmelo Antonio Finocchiaro, University of Catania
