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Approximations and endomorphism algebras of modules /
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 gradual...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; New York :
Walter de Gruyter,
2006.
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| Colección: | De Gruyter expositions in mathematics ;
41. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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
- 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.