Covers and Envelopes in the Category of Complexes of Modules: 1st Edition (Paperback) book cover

Covers and Envelopes in the Category of Complexes of Modules

1st Edition

By J.R. Garcia Rozas

Chapman and Hall/CRC

152 pages

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Paperback: 9781584880042
pub: 1999-05-11
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Description

Over the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. 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.

The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers.

Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes.

Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results.

Table of Contents

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

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General
MAT022000
MATHEMATICS / Number Theory