Integral closure of ideals, rings, and modules

Author(s)

• Huneke, Craig
• Swanson, Irena

Bibliographic Information

Integral closure of ideals, rings, and modules

Craig Huneke, Irena Swanson

（London Mathematical Society lecture note series, 336）

Cambridge University Press, 2006

• : pbk

Note

Includes bibliographical references (p. [405]-421) and index

Description and Table of Contents

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 Briancon-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.

Table of Contents

• Table of basic properties
• Notation and basic definitions
• Preface
• 1. What is the integral closure
• 2. Integral closure of rings
• 3. Separability
• 4. Noetherian rings
• 5. Rees algebras
• 6. Valuations
• 7. Derivations
• 8. Reductions
• 9. Analytically unramified rings
• 10. Rees valuations
• 11. Multiplicity and integral closure
• 12. The conductor
• 13. The Briancon-Skoda theorem
• 14. Two-dimensional regular local rings
• 15. Computing the integral closure
• 16. Integral dependence of modules
• 17. Joint reductions
• 18. Adjoints of ideals
• 19. Normal homomorphisms
• Appendix A. Some background material
• Appendix B. Height and dimension formulas
• References
• Index.

by "Nielsen BookData"

Details

• NCID: BA78652692
• ISBN:
  • 0521688604
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge, UK
• Pages/Volumes: xiv, 431 p.
• Size: 23 cm
• Classification:
  • DC22 : 512.44
• Subject Headings:
  • LCSH : Integral closure
  • LCSH : Ideals (Algebra)
  • LCSH : Commutative rings
  • LCSH : Modules (Algebra)
• Parent Bibliography ID:
  • BA0005393X