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  • 1
    Online Resource
    Online Resource
    Non-Noetherian Commutative Ring Theory (2000)
    Boston, MA :Springer US :
    Details
    UID:
    almahu_9947363214302882
    Format: X, 480 p. , online resource.
    ISBN: 9781475731804
    Series Statement: Mathematics and Its Applications ; 520
    Content: Commutative Ring Theory emerged as a distinct field of research in math­ ematics only at the beginning of the twentieth century. It is rooted in nine­ teenth century major works in Number Theory and Algebraic Geometry for which it provided a useful tool for proving results. From this humble origin, it flourished into a field of study in its own right of an astonishing richness and interest. Nowadays, one has to specialize in an area of this vast field in order to be able to master its wealth of results and come up with worthwhile contributions. One of the major areas of the field of Commutative Ring Theory is the study of non-Noetherian rings. The last ten years have seen a lively flurry of activity in this area, including: a large number of conferences and special sections at national and international meetings dedicated to presenting its results, an abundance of articles in scientific journals, and a substantial number of books capturing some of its topics. This rapid growth, and the occasion of the new Millennium, prompted us to embark on a project aimed at presenting an overview of the recent research in the area. With this in mind, we invited many of the most prominent researchers in Non-Noetherian Commutative Ring Theory to write expository articles representing the most recent topics of research in this area.
    Note: 1 GCD Domains, Gauss’ Lemma, and Contents of Polynomials -- 2 The Class Group and Local Class Group of an Integral Domain -- 3 Mori Domains -- 4 What’s New About Integer-Valued Polynomials on a Subset? -- 5 Half-Factorial Domains, a Survey -- 6 On Generalized Lengths of Factorizations in Dedekind and Krull Domains -- 7 Recent Progress on Going-Down I -- 8 Localizing Systems and Semistar Operations -- 9 Ideal Theory in Pullbacks -- 10 Commutative Rings of Dimension 0 -- 11 Finite Conductor Rings with Zero Divisors -- 12 Construction of Ideal Systems with Nice Noetherian Properties -- 13 Generalized Local Rings and Finite Generation of Powers of Ideals -- 14 Connecting Trace Properties -- 15 Constructing Examples of Integral Domains by Intersecting Valuation Domains -- 16 Examples Built With D+M, A+XB[X] and Other Pullback Constructions -- 17 T-Closedness -- 18 E-rings and Related Structures -- 19 Prime Ideals and Decompositions of Modules -- 20 Putting t-Invertibility to Use -- 21 One Hundred Problems in Commutative Ring Theory.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781441948359
    Language: English
    Keywords: Aufsatzsammlung
    DOI: 10.1007/978-1-4757-3180-4
    URL: http://dx.doi.org/10.1007/978-1-4757-3180-4
    URL: Volltext
    URL: Volltext  (lizenzpflichtig)
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  • 2
    Online Resource
    Online Resource
    Progress in Commutative Algebra 2 : Closures, Finiteness and Factorization (2012)
    Berlin ;Boston :De Gruyter,
    Details
    UID:
    almafu_9958353916502883
    Format: 1 online resource (325p.)
    ISBN: 9783110278606
    Series Statement: De Gruyter Proceedings in Mathematics
    Content: This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.
    Note: Frontmatter -- , Preface -- , Contents -- , A Guide to Closure Operations in Commutative Algebra -- , A Survey of Test Ideals -- , Finite-dimensional Vector Spaces with Frobenius Action -- , Finiteness and Homological Conditions in Commutative Group Rings -- , Regular Pullbacks -- , Noetherian Rings without Finite Normalization -- , Krull Dimension of Polynomial and Power Series Rings -- , The Projective Line over the Integers -- , On Zero Divisor Graphs -- , A Closer Look at Non-Unique Factorization via Atomic Decay and Strong Atoms , In English.
    Additional Edition: ISBN 978-3-11-027859-0
    Language: English
    DOI: 10.1515/9783110278606
    URL: https://doi.org/10.1515/9783110278606
    URL: https://doi.org/10.1515/9783110278606
    URL: Cover
    URL: Open Access
    URL: Open Access
    URL: Cover
    Library Location Call Number Volume/Issue/Year Availability
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    HU Berlin
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  • 3
    Book
    Book
    Non-Noetherian commutative ring theory (2000)
    Dordrecht [u.a.] : Kluwer Academic Publishers
    Details
    UID:
    gbv_315801514
    Format: X, 479 S
    ISBN: 0792364929 , 9780792364924
    Series Statement: Mathematics and its applications 〈Dordrecht〉 520
    Note: Includes index , Includes bibliographical references and index
    Language: English
    Subjects: Mathematics
    RVK:
    SK 230
    Keywords: Kommutativer Ring ; Kommutativer Ring ; Kommutativer Ring ; Noetherscher Ring ; Aufsatzsammlung ; Aufgabensammlung
    URL: Inhaltsverzeichnis
    URL: Klappentext
    URL: Inhaltstext
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    Book
    Stabi Berlin get availability status
  • 4
    Online Resource
    Online Resource
    Progress in Commutative Algebra 2 : Closures, Finiteness and Factorization (2012)
    Berlin ;Boston :De Gruyter,
    Details
    UID:
    edocfu_9958353916502883
    Format: 1 online resource (325p.)
    ISBN: 9783110278606
    Series Statement: De Gruyter Proceedings in Mathematics
    Content: This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.
    Note: Frontmatter -- , Preface -- , Contents -- , A Guide to Closure Operations in Commutative Algebra -- , A Survey of Test Ideals -- , Finite-dimensional Vector Spaces with Frobenius Action -- , Finiteness and Homological Conditions in Commutative Group Rings -- , Regular Pullbacks -- , Noetherian Rings without Finite Normalization -- , Krull Dimension of Polynomial and Power Series Rings -- , The Projective Line over the Integers -- , On Zero Divisor Graphs -- , A Closer Look at Non-Unique Factorization via Atomic Decay and Strong Atoms , In English.
    Additional Edition: ISBN 978-3-11-027859-0
    Language: English
    DOI: 10.1515/9783110278606
    URL: https://doi.org/10.1515/9783110278606
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    FU Berlin
  • 5
    Online Resource
    Online Resource
    Progress in Commutative Algebra 2 : Closures, Finiteness and Factorization (2012)
    Berlin/Boston : De Gruyter, Inc.
    Details
    UID:
    gbv_1658077954
    Format: 1 online resource (315 pages)
    ISBN: 9783110278606
    Series Statement: De Gruyter Proceedings in Mathematics Ser
    Content: 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.
    Content: 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.
    Note: Description based on publisher supplied metadata and other sources
    Additional Edition: ISBN 9783110278590
    Additional Edition: Erscheint auch als Druck-Ausgabe Progress in commutative algebra ; 2: Closures, finiteness and factorization Berlin [u.a.] : De Gruyter, 2012 ISBN 9783110278590
    Language: German
    URL: Volltext  (lizenzpflichtig)
    URL: Inhaltstext
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    Online Access
    UB Potsdam
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