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Model Theory of Modules, Algebras and Categories
This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy. Papers contained in this volume cover recent developments in m...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1929.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Contents; Chapter 1. Preface; On isonoetherian and isoartinian modules; 1. Introduction; 2. Isosimple modules; 3. Isonoetherian and isoartinian modules and rings; 4. Isoradical of a ring and modules generated by isosimpe modules; 5. Modules of finite I-length; Acknowledgment; References; Derived categories for Grothendieck categories of enriched functors; 1. Introduction; 2. Enriched Category Theory; 3. The closed symmetric monoidal structure for chain complexes; 4. The enriched structure; 5. Identifying chain complexes with enriched functors
- 6. Compact generators for the derived categoryReferences; Left determined morphisms and free realisations; 1. Basic concepts; 2. The relationship between free realisations and determiners; 3. A proof of the existence of left determiners for morphisms; Acknowledgments; References; The universal abelian regular ring; 1. The group inverse; 2. Olivier's construction; 3. Definable scalars of -rings.; 4. The commutative case; 5. The lattice of pp definable subgroups; 6. The constructible Cohn spectrum; 7. The Ziegler spectrum; 8. The étale bundle of definable scalars; Acknowledgement; References
- A characterisation of -tilting finite algebrasIntroduction; 1. Silting modules and ring epimorphisms; 2. From torsion classes to abelian subcategories; 3. From abelian subcategories to torsion classes; 4.-tilting finite algebras; References; Describing models of Th($! in adelic terms; 1. Introduction; 2. Applying the long exact sequence; 3. Conclusions; References; Valued modules on skew polynomial rings and Bézout domains; 1. Introduction; 2. Preliminaries; 3. Valued modules; 4. Valued Ore modules; 5. Valued modules over a Bézout domain; References
- Multisorted modules and their model theory1. Introduction; 2. Multisorted modules, quiver representations and additive functors; 3. Setting up linear algebra in multisorted modules; 4. Modules in any abelian category; 5. Multisorted modules as structures; 6. Examples of multisorted modules; 7. Adding new sorts; 8. Three categories; 9. An example: ₃; 10. Adding more conditions: localisation and definable subcategories; 11. An example: ₃ again; 12. Further examples: triangulated categories; 13. Further examples: Nori motives; 14. Extending tensor product to sorts; an example; References
- Pure projective modules over non-singular serial rings1. Introduction; 2. Basics on uniserial modules; 3. Finitely presented modules over serial rings; 4. Dimension theory for pure projective modules over serial rings; 5. The main result; References; Mittag-Leffler modules and definable subcategories; 1. Introduction; 2. Preliminaries; 3. Mittag-Leffler modules; 4. Special cases; 5. Purity; 6. Pure separation; 7. Countably generated modules; Acknowledgments; References; Intrinsic valuation entropy; 1. Introduction; 2. Definitions and preliminary facts