ENGLISH

Integral closure of ideals, rings, and modules

By Craig Huneke , Irena Swanson

Book information

Publisher
Cambridge University Press
Year
2006
ISBN
0521688604, 9780521688604
Open Library ID
OL7752087M
Language
english
Format
PDF
Filesize
3 MB (3215924 bytes)
Series
London Mathematical Society lecture note series 336
Edition
web draft
Pages
446\446
Topic
Mathematics Algebra
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

Integral closure has played a role in number theory and algebraic geometry since the nineteenth century, but a modern formulation of the concept for ideals perhaps began with the work of Krull and Zariski in the 1930s. It has developed into a tool for the analysis of many algebraic and geometric problems. This book collects together the central notions of integral closure and presents a unified treatment. Techniques and topics covered include: behavior of the Noetherian property under integral closure, analytically unramified rings, the conductor, field separability, valuations, Rees algebras, Rees valuations, reductions, multiplicity, mixed multiplicity, joint reductions, the Briançon-Skoda theorem, Zariski's theory of integrally closed ideals in two-dimensional regular local rings, computational aspects, adjoints of ideals and normal homomorphisms. With many worked examples and exercises, this book will provide graduate students and researchers in commutative algebra or ring theory with an approachable introduction leading into the current literature.

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