Softcover ISBN:  9781470466428 
Product Code:  SURV/259 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470467333 
Product Code:  SURV/259.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470466428 
eBook: ISBN:  9781470467333 
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:  9781470466428 
Product Code:  SURV/259 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470467333 
Product Code:  SURV/259.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470466428 
eBook ISBN:  9781470467333 
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 

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.

Table of Contents

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

Heightone 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

NonNoetherian examples of dimension 3

Noetherian properties of nonNoetherian rings

NonNoetherian examples in higher dimension

The Homomorphic Image Construction

Catenary local rings with geometrically normal fibers

An Ogomalike example

Multiidealadic completions of Noetherian rings

Noetherian flatness and multiadic 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 polynomialpower series rings

Mixed polynomialpower series rings and relations among their spectra

Extensions of local domains with trivial generic fiber

Constructions and examples discussed in this book


Additional Material

Reviews

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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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

Heightone 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

NonNoetherian examples of dimension 3

Noetherian properties of nonNoetherian rings

NonNoetherian examples in higher dimension

The Homomorphic Image Construction

Catenary local rings with geometrically normal fibers

An Ogomalike example

Multiidealadic completions of Noetherian rings

Noetherian flatness and multiadic 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 polynomialpower series rings

Mixed polynomialpower 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