Model theory of modules, algebras and categories : International Conference on Model Theory of Modules, Algebras, and Categories, July 28-August 2, 2017, Ettore Majorana Foundation and Centre for Scientific Culture, Erice, Sicily, Italy / Alberto Facchini [and three others], editors.

Format:

Book

Conference/Event

Author/Creator:

Facchini, Alberto.

Contributor:

Facchini, Alberto, editor.

Conference Name:

International Conference on Model Theory of Modules, Algebras, and Categories (2017 : Erice, Italy), author.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 730

Contemporary mathematics, 730 0271-4132

Language:

English

Subjects (All):

Modules (Algebra)--Congresses.

Modules (Algebra).

Algebra--Congresses.

Algebra.

Physical Description:

1 online resource (vii, 237 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2019]

Language Note:

English

Summary:

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 model theory, module theory and category theory, and their intersection.

Contents:

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

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 category

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

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

A characterisation of -tilting finite algebras

Introduction

1. Silting modules and ring epimorphisms

2. From torsion classes to abelian subcategories

3. From abelian subcategories to torsion classes

4. -tilting finite algebras

Describing models of Th(ℤ) in adelic terms

2. Applying the long exact sequence

3. Conclusions

Valued modules on skew polynomial rings and Bézout domains

2. Preliminaries

3. Valued modules

4. Valued Ore modules

5. Valued modules over a Bézout domain

References.

Multisorted modules and their model theory

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

Pure projective modules over non-singular serial rings

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

Mittag-Leffler modules and definable subcategories

3. Mittag-Leffler modules

4. Special cases

5. Purity

6. Pure separation

7. Countably generated modules

Intrinsic valuation entropy

2. Definitions and preliminary facts

3. Some tools for the computation of entropy

4. The Addition Theorem

5. The Intrinsic Algebraic Yuzvinski Formula

6. The Uniqueness Theorem

Decidability and modules over Bézout domains

2. Basic facts on modules

3. Intermezzo

4. Bézout domains

5. The main theorem

6. From Bézout to Prüfer

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-5295-2