Covers and Envelopes in the Category of Complexes of Modules

1. Auflage 1999
ISBN: 978-1-58488-004-2
Verlag: Chapman and Hall/CRC

Buch, Englisch, 152 Seiten, Format (B × H): 154 mm x 235 mm, Gewicht: 227 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

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.

Zielgruppe

Professional

Autoren/Hrsg.

Rozas, J. R. Garcia

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

Covers and Envelopes in CategoriesZorn's Lemma for CategoriesTorsion Theory Relative to ExtPreserving and Reflecting Covers by FunctorsOrthogonality in the Category of ComplexesIntroductionSpaltenstein's Quasi-IsomorphismsExact, DG-Injective and DG Projective Covers and EnvelopesMinimal Injective ResolutionsGorenstein Injective and Gorenstein Projective ComplexesPreliminariesGorenstein Injective ComplexesGorenstein Projective ComplexesFlat and DG-Flat ComplexesFirst Definitions and ResultsSome Canonical IsomorphismsFlat Covers of ComplexesExistence of Flat Covers of Complexes over a Commutative Noetherian Ring with Finite Krull DimensionPure Sequences of ComplexesPreliminariesFlat Pre-Envelope of ComplexesPure Injective and Cotorsion EnvelopesGorenstein Flat ComplexesA Theorem on Perfect RingsDG-Pure SequencesBibliographyIndex

Über Autor(innen)

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