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The Resource Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource)
Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource)
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The item Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure
 Language

 eng
 eng
 Extent
 1 online resource (448 p.)
 Note
 Description based upon print version of record
 Contents

 Cover; Series Page; Title; Copyright; Contents; Table of basic properties; Notation and basic definitions; Preface; 1 What is integral closure of ideals?; 1.1. Basic properties; 1.2. Integral closure via reductions; 1.3. Integral closure of an ideal is an ideal; 1.4. Monomial ideals; 1.5. Integral closure of rings; 1.6. How integral closure arises; 1.7. DedekindMertens formula; 1.8. Exercises; 2 Integral closure of rings; 2.1. Basic facts; 2.2. LyingOver, Incomparability, GoingUp, GoingDown; 2.3. Integral closure and grading; 2.4. Rings of homomorphisms of ideals; 2.5. Exercises
 3 Separability3.1. Algebraic separability; 3.2. General separability; 3.3. Relative algebraic closure; 3.4. Exercises; 4 Noetherian rings; 4.1. Principal ideals; 4.2. Normalization theorems; 4.3. Complete rings; 4.4. Jacobian ideals; 4.5. Serre's conditions; 4.6. Affine and Zalgebras; 4.7. Absolute integral closure; 4.8. Finite LyingOver and height; 4.9. Dimension one; 4.10. Krull domains; 4.11. Exercises; 5 Rees algebras; 5.1. Rees algebra constructions; 5.2. Integral closure of Rees algebras; 5.3. Integral closure of powers of an ideal; 5.4. Powers and formal equidimensionality
 5.5. Defining equations of Rees algebras5.6. Blowing up; 5.7. Exercises; 6 Valuations; 6.1. Valuations; 6.2. Value groups and valuation rings; 6.3. Existence of valuation rings; 6.4. More properties of valuation rings; 6.5. Valuation rings and completion; 6.6. Some invariants; 6.7. Examples of valuations; 6.8. Valuations and the integral closure of ideals; 6.9. The asymptotic Samuel function; 6.10. Exercises; 7 Derivations; 7.1. Analytic approach; 7.2. Derivations and differentials; 7.3. Exercises; 8 Reductions; 8.1. Basic properties and examples; 8.2. Connections with Rees algebras
 8.3. Minimal reductions8.4. Reducing to infinite residue fields; 8.5. Superficial elements; 8.6. Superficial sequences and reductions; 8.7. Nonlocal rings; 8.8. Sally's theorem on extensions; 8.9. Exercises; 9 Analytically unramified rings; 9.1. Rees's characterization; 9.2. Modulefinite integral closures; 9.3. Divisorial valuations; 9.4. Exercises; 10 Rees valuations; 10.1. Uniqueness of Rees valuations; 10.2. A construction of Rees valuations; 10.3. Examples; 10.4. Properties of Rees valuations; 10.5. Rational powers of ideals; 10.6. Exercises; 11 Multiplicity and integral closure
 11.1. HilbertSamuel polynomials11.2. Multiplicity; 11.3. Rees's theorem; 11.4. Equimultiple families of ideals; 11.5. Exercises; 12 The conductor; 12.1. A classical formula; 12.2. Onedimensional rings; 12.3. The LipmanSathaye theorem; 12.4. Exercises; 13 The BriançonSkoda Theorem; 13.1. Tight closure; 13.2. BriançonSkoda via tight closure; 13.3. The LipmanSathaye version; 13.4. General version; 13.5. Exercises; 14 Twodimensional regular local rings; 14.1. Full ideals; 14.2. Quadratic transformations; 14.3. The transform of an ideal; 14.4. Zariski's theorems
 14.5. A formula of Hoskin and Deligne
 Isbn
 9781107095557
 Label
 Integral closure of ideals, rings, and modules
 Title
 Integral closure of ideals, rings, and modules
 Statement of responsibility
 Craig Huneke, Irena Swanson
 Language

 eng
 eng
 Summary
 Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure
 Cataloging source
 MiAaPQ
 http://library.link/vocab/creatorName
 Huneke, C.
 Dewey number
 512.44
 Illustrations
 illustrations
 Index
 index present
 Language note
 English
 LC call number
 QA251.3
 LC item number
 .H86 2006
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Swanson, Irena
 Series statement

 London Mathematical Society lecture note series
 London Mathematical Society Lecture Note Series
 Series volume
 336
 http://library.link/vocab/subjectName

 Integral closure
 Ideals (Algebra)
 Commutative rings
 Modules (Algebra)
 Label
 Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [405]421) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Cover; Series Page; Title; Copyright; Contents; Table of basic properties; Notation and basic definitions; Preface; 1 What is integral closure of ideals?; 1.1. Basic properties; 1.2. Integral closure via reductions; 1.3. Integral closure of an ideal is an ideal; 1.4. Monomial ideals; 1.5. Integral closure of rings; 1.6. How integral closure arises; 1.7. DedekindMertens formula; 1.8. Exercises; 2 Integral closure of rings; 2.1. Basic facts; 2.2. LyingOver, Incomparability, GoingUp, GoingDown; 2.3. Integral closure and grading; 2.4. Rings of homomorphisms of ideals; 2.5. Exercises
 3 Separability3.1. Algebraic separability; 3.2. General separability; 3.3. Relative algebraic closure; 3.4. Exercises; 4 Noetherian rings; 4.1. Principal ideals; 4.2. Normalization theorems; 4.3. Complete rings; 4.4. Jacobian ideals; 4.5. Serre's conditions; 4.6. Affine and Zalgebras; 4.7. Absolute integral closure; 4.8. Finite LyingOver and height; 4.9. Dimension one; 4.10. Krull domains; 4.11. Exercises; 5 Rees algebras; 5.1. Rees algebra constructions; 5.2. Integral closure of Rees algebras; 5.3. Integral closure of powers of an ideal; 5.4. Powers and formal equidimensionality
 5.5. Defining equations of Rees algebras5.6. Blowing up; 5.7. Exercises; 6 Valuations; 6.1. Valuations; 6.2. Value groups and valuation rings; 6.3. Existence of valuation rings; 6.4. More properties of valuation rings; 6.5. Valuation rings and completion; 6.6. Some invariants; 6.7. Examples of valuations; 6.8. Valuations and the integral closure of ideals; 6.9. The asymptotic Samuel function; 6.10. Exercises; 7 Derivations; 7.1. Analytic approach; 7.2. Derivations and differentials; 7.3. Exercises; 8 Reductions; 8.1. Basic properties and examples; 8.2. Connections with Rees algebras
 8.3. Minimal reductions8.4. Reducing to infinite residue fields; 8.5. Superficial elements; 8.6. Superficial sequences and reductions; 8.7. Nonlocal rings; 8.8. Sally's theorem on extensions; 8.9. Exercises; 9 Analytically unramified rings; 9.1. Rees's characterization; 9.2. Modulefinite integral closures; 9.3. Divisorial valuations; 9.4. Exercises; 10 Rees valuations; 10.1. Uniqueness of Rees valuations; 10.2. A construction of Rees valuations; 10.3. Examples; 10.4. Properties of Rees valuations; 10.5. Rational powers of ideals; 10.6. Exercises; 11 Multiplicity and integral closure
 11.1. HilbertSamuel polynomials11.2. Multiplicity; 11.3. Rees's theorem; 11.4. Equimultiple families of ideals; 11.5. Exercises; 12 The conductor; 12.1. A classical formula; 12.2. Onedimensional rings; 12.3. The LipmanSathaye theorem; 12.4. Exercises; 13 The BriançonSkoda Theorem; 13.1. Tight closure; 13.2. BriançonSkoda via tight closure; 13.3. The LipmanSathaye version; 13.4. General version; 13.5. Exercises; 14 Twodimensional regular local rings; 14.1. Full ideals; 14.2. Quadratic transformations; 14.3. The transform of an ideal; 14.4. Zariski's theorems
 14.5. A formula of Hoskin and Deligne
 Dimensions
 unknown
 Extent
 1 online resource (448 p.)
 Form of item
 online
 Isbn
 9781107095557
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)2550000001095225
 (EBL)1179159
 (OCoLC)850149065
 (SSID)ssj0000915879
 (PQKBManifestationID)12387962
 (PQKBTitleCode)TC0000915879
 (PQKBWorkID)10869918
 (PQKB)10937181
 (MiAaPQ)EBC1179159
 (EXLCZ)992550000001095225
 Label
 Integral closure of ideals, rings, and modules, Craig Huneke, Irena Swanson, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [405]421) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Cover; Series Page; Title; Copyright; Contents; Table of basic properties; Notation and basic definitions; Preface; 1 What is integral closure of ideals?; 1.1. Basic properties; 1.2. Integral closure via reductions; 1.3. Integral closure of an ideal is an ideal; 1.4. Monomial ideals; 1.5. Integral closure of rings; 1.6. How integral closure arises; 1.7. DedekindMertens formula; 1.8. Exercises; 2 Integral closure of rings; 2.1. Basic facts; 2.2. LyingOver, Incomparability, GoingUp, GoingDown; 2.3. Integral closure and grading; 2.4. Rings of homomorphisms of ideals; 2.5. Exercises
 3 Separability3.1. Algebraic separability; 3.2. General separability; 3.3. Relative algebraic closure; 3.4. Exercises; 4 Noetherian rings; 4.1. Principal ideals; 4.2. Normalization theorems; 4.3. Complete rings; 4.4. Jacobian ideals; 4.5. Serre's conditions; 4.6. Affine and Zalgebras; 4.7. Absolute integral closure; 4.8. Finite LyingOver and height; 4.9. Dimension one; 4.10. Krull domains; 4.11. Exercises; 5 Rees algebras; 5.1. Rees algebra constructions; 5.2. Integral closure of Rees algebras; 5.3. Integral closure of powers of an ideal; 5.4. Powers and formal equidimensionality
 5.5. Defining equations of Rees algebras5.6. Blowing up; 5.7. Exercises; 6 Valuations; 6.1. Valuations; 6.2. Value groups and valuation rings; 6.3. Existence of valuation rings; 6.4. More properties of valuation rings; 6.5. Valuation rings and completion; 6.6. Some invariants; 6.7. Examples of valuations; 6.8. Valuations and the integral closure of ideals; 6.9. The asymptotic Samuel function; 6.10. Exercises; 7 Derivations; 7.1. Analytic approach; 7.2. Derivations and differentials; 7.3. Exercises; 8 Reductions; 8.1. Basic properties and examples; 8.2. Connections with Rees algebras
 8.3. Minimal reductions8.4. Reducing to infinite residue fields; 8.5. Superficial elements; 8.6. Superficial sequences and reductions; 8.7. Nonlocal rings; 8.8. Sally's theorem on extensions; 8.9. Exercises; 9 Analytically unramified rings; 9.1. Rees's characterization; 9.2. Modulefinite integral closures; 9.3. Divisorial valuations; 9.4. Exercises; 10 Rees valuations; 10.1. Uniqueness of Rees valuations; 10.2. A construction of Rees valuations; 10.3. Examples; 10.4. Properties of Rees valuations; 10.5. Rational powers of ideals; 10.6. Exercises; 11 Multiplicity and integral closure
 11.1. HilbertSamuel polynomials11.2. Multiplicity; 11.3. Rees's theorem; 11.4. Equimultiple families of ideals; 11.5. Exercises; 12 The conductor; 12.1. A classical formula; 12.2. Onedimensional rings; 12.3. The LipmanSathaye theorem; 12.4. Exercises; 13 The BriançonSkoda Theorem; 13.1. Tight closure; 13.2. BriançonSkoda via tight closure; 13.3. The LipmanSathaye version; 13.4. General version; 13.5. Exercises; 14 Twodimensional regular local rings; 14.1. Full ideals; 14.2. Quadratic transformations; 14.3. The transform of an ideal; 14.4. Zariski's theorems
 14.5. A formula of Hoskin and Deligne
 Dimensions
 unknown
 Extent
 1 online resource (448 p.)
 Form of item
 online
 Isbn
 9781107095557
 Media category
 computer
 Media type code

 c
 Specific material designation
 remote
 System control number

 (CKB)2550000001095225
 (EBL)1179159
 (OCoLC)850149065
 (SSID)ssj0000915879
 (PQKBManifestationID)12387962
 (PQKBTitleCode)TC0000915879
 (PQKBWorkID)10869918
 (PQKB)10937181
 (MiAaPQ)EBC1179159
 (EXLCZ)992550000001095225
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