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.

First comprehensive book treatment of topic

Autorentext

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.

Inhalt
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.- HowTo.