Purity, spectra and localisation / Mike Prest.

Format:

Book

Author/Creator:

Prest, Mike, author.

Series:

Encyclopedia of mathematics and its applications ; v. 121.

Encyclopedia of mathematics and its applications ; volume 121

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Categories (Mathematics).

Physical Description:

1 online resource (xxviii, 769 pages) : digital, PDF file(s).

Other Title:

Purity, Spectra & Localisation

Place of Publication:

Cambridge : Cambridge University Press, 2009.

Language Note:

English

Summary:

It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.

Contents:

Pp conditions

Purity

Pp-pairs and definable subcategories

Pp-types and pure-injectivity

The Ziegler spectrum

Rings of definable scalars

M-dimension and width

Examples

Ideals in mod-R

Finitely presented functors

Serre subcategories and localisation

The Ziegler spectrum and injective functors

Dimensions

The Zariski spectrum and the sheaf of definable scalars

Artin algebras

Finitely accessible and presentable additive categories

Spectra of triangulated categories

Definable categories and interpretation functors.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88709-2

1-139-63540-9

1-139-63754-1

1-139-64424-6

1-139-64930-2

1-139-64168-9

1-139-63884-X

1-139-64834-9

OCLC:

853360223