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Integral Closure

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Integral Closure Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. 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.

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.

Table of Contents

Preface.- Introduction.- Numerical Invariants of a Rees Algebra.- Hilbert Functions and Multiplicities.- Depth and Cohomology of Rees Algebras.- Divisors of a Rees Algebra.- Koszul Homology.- Integral Closure of Algebras.- Integral Closure and Normalization of Ideals.- Integral Closure of Modules.- How To.- References.- Notation and Terminology.- Index.

Product Details

ISBN:
9783540255406
Publisher:
Springer
Subject:
Algebra
Author:
Vasconcelos, Wolmer
Subject:
Algebra - General
Subject:
Commutative algebra
Subject:
Algebraic Geometry
Subject:
computational algebra
Subject:
Rees algebras
Subject:
Commutative Rings and Algebras
Subject:
Geometry - Algebraic
Subject:
Number Theory
Subject:
Algebra - Abstract
Subject:
Mathematics-Abstract Algebra
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Springer Monographs in Mathematics
Publication Date:
June 2005
Binding:
HARDCOVER
Language:
English
Illustrations:
3 schw.-w. Tab.
Pages:
532
Dimensions:
235 x 155 mm

Related Subjects

Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Number Theory

Integral Closure
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Product details 532 pages Springer - English 9783540255406 Reviews:
"Synopsis" by , This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. 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.
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