Authors:
- First comprehensive book treatment of topic
Part of the book series: Springer Monographs in Mathematics (SMM)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
About this book
Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.
This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported.
Reviews
From the reviews:
"Wolmer Vasconocelos is an authoritative figure in commutative algebra today. … The book under review is an important undertaking and will likely represent an essential research tool for generations to come as well as a standard reference text. … The book is a tour de force in commutative algebra … . Wolmer Vasconcelos does a wonderful job presenting the big picture surrounding the concepts … . This book is recommended to graduate students and mathematicians … . It represents a great addition to the literature." (Florian Enescu, Zentralblatt MATH, Vol. 1082, 2006)
"Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. … It gives a comprehensive treatment of Rees algebra and multiplicity theory – while pointing to applications in many other problem areas. … This book is intended for graduate students and researchers in the fields mentioned above. It contains, besides exercises aimed at giving insights, numerous research problems motivated by the developments reported." (L’Enseignement Mathematique, Vol. 51 (3-4), 2005)
"The aim of this book is to provide a systematic account of several recent developments on integral closures of ideals and modules in many guises. … This book is addressed to readers who are familiar with basic concepts of commutative algebra, and it could be used for an advanced course … . Graduate students and researchers will find this book useful as a standard reference text on blowup algebras. It contains, besides exercises aimed at giving insights, numerous research problems motivated by recent developments." (Ngô Viêt Trung, Mathematical Reviews, Issue 2006 m)
Authors and Affiliations
-
Department of Mathematics, Rutgers University, Piscataway, USA
Wolmer Vasconcelos
About the author
Author's homepage: http://www.math.rutgers.edu/~vasconce/
Vasconcelos is a well-known top expert in commutative algebra. Author of Algorithms and Computation in Mathematics 2. ISBN: 3-540-21311-2.
Via the existence of the ACM series he was won as a Springer author in 1995, being a CUP author before.
This new book is a result of the good collaboration with him on ACM 2.
Bibliographic Information
Book Title: Integral Closure
Book Subtitle: Rees Algebras, Multiplicities, Algorithms
Authors: Wolmer Vasconcelos
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/b137713
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Hardcover ISBN: 978-3-540-25540-6Published: 23 May 2005
Softcover ISBN: 978-3-642-06492-0Published: 21 October 2010
eBook ISBN: 978-3-540-26503-0Published: 04 November 2005
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XII, 520
Topics: Commutative Rings and Algebras, Algebraic Geometry, Number Theory