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Cover: 9780521688604 | Integral Closure of Ideals, Rings, and Modules | Craig Huneke (u. a.)
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Integral Closure of Ideals, Rings, and Modules
Taschenbuch von Craig Huneke (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Irena Swanson is a Professor in the Department of Mathematics at Reed College, Portland.
Inhaltsverzeichnis
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 Briançon-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.
Details
Medium: Taschenbuch
Seiten: 448
ISBN-13: 9780521688604
ISBN-10: 0521688604
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Huneke, Craig
Swanson, Irena
Hersteller: Cambridge University Press
Maße: 229 x 152 x 26 mm
Von/Mit: Craig Huneke (u. a.)
Erscheinungsdatum: 31.03.2008
Gewicht: 0,722 kg
preigu-id: 102132037
Über den Autor
Irena Swanson is a Professor in the Department of Mathematics at Reed College, Portland.
Inhaltsverzeichnis
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 Briançon-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.
Details
Medium: Taschenbuch
Seiten: 448
ISBN-13: 9780521688604
ISBN-10: 0521688604
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Huneke, Craig
Swanson, Irena
Hersteller: Cambridge University Press
Maße: 229 x 152 x 26 mm
Von/Mit: Craig Huneke (u. a.)
Erscheinungsdatum: 31.03.2008
Gewicht: 0,722 kg
preigu-id: 102132037
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