| Description |
1 online resource (xxiv, 640 pages) |
| Series |
De Gruyter expositions in mathematics, 0938-6572 ; 41 |
|
De Gruyter expositions in mathematics ; 41. 0938-6572
|
| Contents |
Chapter 1; 1.1 S-completions; 1.2 Pure-injective modules; 1.3 Locally projective modules; 1.4 Factors of products and slender modules; 1.5 Slender modules over Dedekind domains; Chapter 2; 2.1 Preenvelopes and precovers; 2.2 Cotorsion pairs and Tor-pairs; 2.3 Minimal approximations; Chapter 3; 3.1 Ext and direct limits; 3.2 The variety of complete cotorsion pairs; 3.3 Ext and inverse limits; Chapter 4; 4.1 Approximations by modules of finite homological di-mensions; 4.2 Hill Lemma and Kaplansky Theorem for cotorsion pairs; 4.3 Closure properties providing for completeness |
|
880-01 8.2 1-cotilting modules and cotilting torsion-free classesChapter 9; 9.1 Survey of prediction principles using ZFC and more; 9.2 The Black Boxes; 9.3 The Shelah Elevator; Chapter 10; 10.1 Completeness of cotorsion pairs under the Diamond Principle; 10.2 Uniformization and cotorsion pairs not generated by a set; Chapter 11; 11.1 Ultra-cotorsion-free modules and the Strong Black Box; 11.2 Rational cotorsion pairs; 11.3 Embedding posets into the lattice of cotorsion pairs; Chapter 12; 12.1 Realizing algebras of size ≤ 2ℵ; 12.2 ℵ1-free modules of cardinality ℵ |
|
880-01/(S 4.4 Matlis cotorsion and strongly flat modules4.5 The closure of a cotorsion pair; Chapter 5; 5.1 Tilting modules; 5.2 Classes of finite type; 5.3 Injectivity properties of tilting modules; Chapter 6; 6.1 Tilting torsion classes; 6.2 The structure of tilting modules and classes over par-ticular rings; 6.3 Matlis localizations; Chapter 7; 7.1 Finitistic dimension conjectures and the tilting mod-ule; 7.2 A formula for the little finitistic dimension of right artinian rings; 7.3 Artinian rings with P <ω contravariantly finite; Chapter 8; 8.1 Cotilting classes and the classes of cofinite type |
|
12.3 Realizing all cotorsion-free algebras12.4 Algebras of row-and-column-finite matrices; Chapter 13; 13.1 Classical; 13.2 Constructing torsion-free, reduced of rank d"25! 13.3; 13.4; 13.5 Discussing 5!-free; 13.6 Mixed; 13.7; 13.8 Generalized; 13.9 Model theory for generalized; 13.10 Constructing proper generalized; Chapter 14; 14.1 The five-submodule theorem, an easy application of the elevator; 14.2 The four-submodule theorem, a harder case; 14.3 A discussion of representations of posets; 14.4 Absolutely indecomposable modules; 14.5 Passing to R-modules |
|
14.6 A topological realization from Theorem 14.2.12Chapter 15; 15.1 Leavitt type rings: the discrete case; 15.2 Automorphism groups of torsion-free abelian groups; 15.3 Algebras with a Hausdorff topology; 15.4 Realizing particular algebras as endomorphism al-gebras |
| Summary |
Provides a treatment of two important parts of contemporary module theory: approximations of modules and their applications, notably to infinite dimensional tilting theory, and realizations of algebras as endomorphism algebras of groups and modules. This monograph starts from basic facts and gradually develops the theory to its present frontiers |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Modules (Algebra)
|
|
Moduli theory.
|
|
Approximation theory.
|
|
MATHEMATICS -- Algebra -- Intermediate.
|
|
Approximation theory
|
|
Modules (Algebra)
|
|
Moduli theory
|
| Form |
Electronic book
|
| Author |
Trlifaj, Jan.
|
| LC no. |
2006018289 |
| ISBN |
9783110199727 |
|
3110199726 |
|
