Umfang:
1 online resource (315 pages)
ISBN:
9783110278606
Serie:
De Gruyter Proceedings in Mathematics Ser
Inhalt:
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Inhalt:
Intro -- Preface -- A Guide to Closure Operations in Commutative Algebra -- 1 Introduction -- 2 What Is a Closure Operation? -- 2.1 The Basics -- 2.2 Not-quite-closure Operations -- 3 Constructing Closure Operations -- 3.1 Standard Constructions -- 3.2 Common Closures as Iterations of Standard Constructions -- 4 Properties of Closures -- 4.1 Star-, Semi-prime, and Prime Operations -- 4.2 Closures Defined by Properties of (Generic) Forcing Algebras -- 4.3 Persistence -- 4.4 Axioms Related to the Homological Conjectures -- 4.5 Tight Closure and Its Imitators -- 4.6 (Homogeneous) Equational Closures and Localization -- 5 Reductions, Special Parts of Closures, Spreads, and Cores -- 5.1 Nakayama Closures and Reductions -- 5.2 Special Parts of Closures -- 6 Classes of Rings Defined by Closed Ideals -- 6.1 When Is the Zero Ideal Closed? -- 6.2 When Are 0 and Principal Ideals Generated by Non-zerodivisors Closed? -- 6.3 When Are Parameter Ideals Closed (Where R Is Local)? -- 6.4 When Is Every Ideal Closed? -- 7 Closure Operations on (Sub)modules -- 7.1 Torsion Theories -- A Survey of Test Ideals -- 1 Introduction -- 2 Characteristic p Preliminaries -- 2.1 The Frobenius Endomorphism -- 2.2 F-purity -- 3 The Test Ideal -- 3.1 Test Ideals of Map-pairs -- 3.2 Test Ideals of Rings -- 3.3 Test Ideals in Gorenstein Local Rings -- 4 Connections with Algebraic Geometry -- 4.1 Characteristic 0 Preliminaries -- 4.2 Reduction to Characteristic p 〉 0 and Multiplier Ideals -- 4.3 Multiplier Ideals of Pairs -- 4.4 Multiplier Ideals vs. Test Ideals of Divisor Pairs -- 5 Tight Closure and Applications of Test Ideals -- 5.1 The Briançon-Skoda Theorem -- 5.2 Tight Closure for Modules and Test Elements -- 6 Test Ideals for Pairs (R, αt) and Applications -- 6.1 Initial Definitions of αt -test Ideals -- 6.2 αt -tight Closure -- 6.3 Applications.
Anmerkung:
Description based on publisher supplied metadata and other sources
Weitere Ausg.:
ISBN 9783110278590
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Progress in commutative algebra ; 2: Closures, finiteness and factorization Berlin [u.a.] : De Gruyter, 2012 ISBN 9783110278590
Sprache:
Deutsch
URL:
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