Modules over non-Noetherian domains / László Fuchs, Luigi Salce.

Format:

Book

Author/Creator:

Fuchs, László, author.

Salce, Luigi, author.

Series:

Mathematical surveys and monographs ; no. 84.

Mathematical surveys and monographs, 0076-5376 ; volume 84

Language:

English

Subjects (All):

Modules (Algebra).

Integral domains.

Commutative rings.

Physical Description:

1 online resource (633 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.

Contents:

""Table of Contents""; ""Preface""; ""List of Symbols""; ""Chapter I. Commutative Domains and Their Modules""; ""1. Generalities on domains""; ""2. Fractional ideals""; ""3. Integral dependence""; ""4. Module categories""; ""5. Lemmas on Horn and Ext""; ""6. Lemmas on tensor and torsion products""; ""7. Divisibility and relative divisibility""; ""8. Pure submodules""; ""9. The exchange property""; ""10. Semilocal endomorphism rings""; ""Notes""; ""Chapter II. Valuation Domains""; ""1. Fundamental properties of valuation domains""; ""2. Totally ordered abelian groups""; ""3. Valuations""

""2. Coherent domains""""3. h-Local domains""; ""4. Matlis domains""; ""5. Reflexive domains""; ""Notes""; ""Chapter V. Finitely Generated Modules""; ""1. Cyclic modules""; ""2. Finitely generated modules""; ""3. Finitely presented modules""; ""4. Finite presentations""; ""5. Finitely generated modules over valuation domains""; ""6. Indecomposable finitely generated modules""; ""7. Finitely generated modules with local endomorphism rings""; ""8. Decompositions of finitely generated modules""; ""9. Finitely generated modules without the Krull-Schmidt property""

""Chapter VII. Divisible Modules""""1. Divisible modules""; ""2. h-Divisible modules, Matlis domains""; ""3. Divisible modules over valuation domains""; ""4. Categories of divisible modules""; ""5. Indecomposable divisible modules""; ""6. Superdecomposable divisible modules""; ""Notes""; ""Chapter VIII. Topology and Filtration""; ""1. The R-topology""; ""2. Complete torsion-free modules. The Matlis category equivalence""; ""3. Completions of ideals""; ""4. R-Completions over Matlis domains""; ""5. Cokernels of R-completions""; ""6. Weakly cotorsion modules""; ""7. Linear compactness""

""8. Filtration and ultracompleteness""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 591-602) and indexes.

Description based on print version record.

ISBN:

1-4704-1311-6