Covers and Envelopes in the Category of Complexes of Modules

Over the last few years, the study of complexes has become increasingly important.Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas.

Auteur

J.R. Garcia Rozas (University of Almeria, Spain)

Contenu

Covers and Envelopes in Categories
Zorn's Lemma for Categories
Torsion Theory Relative to Ext
Preserving and Reflecting Covers by Functors
Orthogonality in the Category of Complexes
Introduction
Spaltenstein's Quasi-Isomorphisms
Exact, DG-Injective and DG Projective Covers and Envelopes
Minimal Injective Resolutions
Gorenstein Injective and Gorenstein Projective Complexes
Preliminaries
Gorenstein Injective Complexes
Gorenstein Projective Complexes
Flat and DG-Flat Complexes
First Definitions and Results
Some Canonical Isomorphisms
Flat Covers of Complexes
Existence of Flat Covers of Complexes over a Commutative Noetherian Ring with Finite Krull Dimension
Pure Sequences of Complexes
Preliminaries
Flat Pre-Envelope of Complexes
Pure Injective and Cotorsion Envelopes
Gorenstein Flat Complexes
A Theorem on Perfect Rings
DG-Pure Sequences
Bibliography
Index