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Approximations and Endomorphism Algebras of Modules : Volume 1 - Approximations /
This monograph- now in its second revised and extended edition- provides a thorough treatment of module theory, a subfield of algebra. The authors develop an approximation theory as well as realization theorems and present some of its recent applications, notably to infinite-dimensional combinatoric...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2012.
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| Edición: | 2nd ed. |
| Colección: | De Gruyter expositions in mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 4 Slender modules4.1 Factors of products and slender modules; 4.2 Slender modules over Dedekind domains; 4.3 Open problems; PART II: APPROXIMATIONS AND COTORSION PAIRS ; 5 Approximations of modules; 5.1 Preenvelopes and precovers; 5.2 Cotorsion pairs and Tor-pairs; 5.3 Minimal approximations; 5.4 Open problems; 6 Complete cotorsion pairs; 6.1 Ext and direct limits; 6.2 The abundance of complete cotorsion pairs; 6.3 Ext and inverse limits; 6.4 Open problems; 7 Hill lemma and its applications; 7.1 The general version of the Hill Lemma; 7.2 Kaplansky theorem for cotorsion pairs.
- 7.3 C-socle sequences and Filt.(C)-precovers7.4 Singular compactness for C-filtered modules; 7.5 Ascending and descending properties of modules; 7.6 The rank version of the Hill Lemma; 7.7 Matlis cotorsion and strongly flat modules; 7.8 Open problems; 8 Deconstruction of the roots of Ext; 8.1 Approximations by modules of finite homological dimensions; 8.2 Closure properties providing for deconstruction; 8.3 The closure of a cotorsion pair; 9 Modules of projective dimension one; 9.1 Structure of P 1 and WI for semiprime Goldie rings; 9.2 The class lim P 1; 9.3 Open problems.
- 10 Kaplansky classes and abstract elementary classes10.1 Kaplansky classes and deconstructibility; 10.2 Flat Mittag-Leffler modules revisited; 10.3 Abstract elementary classes of the roots of Ext; 10.4 Open problems; 11 Independence results for cotorsion pairs; 11.1 Completeness of cotorsion pairs under the Diamond Principle; 11.2 Uniformisation and cotorsion pairs not generated by a set; 11.3 Open problems; 12 The lattice of cotorsion pairs; 12.1 Ultra-cotorsion-free modules and the Strong Black Box; 12.2 Rational cotorsion pairs; 12.3 Embedding posets into the lattice of cotorsion pairs.
- PART III: TILTING AND COTILTING APPROXIMATIONS 13 Tilting approximations; 13.1 Tilting modules; 13.2 Classes of finite type; 13.3 Localisation of tilting modules; 13.4 Product-completeness of tilting modules; 13.5 Open problems; 14 1-tilting modules and their applications; 14.1 Tilting torsion classes; 14.2 The structure of 1-tilting modules and classes over particular rings; 14.3 Baer modules; 14.4 Matlis localisations; 14.5 Open problems; 15 Cotilting classes; 15.1 Cotilting classes and the classes of cofinite type; 15.2 1-cotilting modules and cotilting torsion-free classes.