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Flat Covers of Complexes

✍ Scribed by Edgar E Enochs; J.R Garcı́a Rozas


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
158 KB
Volume
210
Category
Article
ISSN
0021-8693

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✦ Synopsis


In this article we define and study flat complexes over any ring. Also, we prove that any complex over a commutative noetherian ring with finite Krull dimension has a flat cover and a DG-flat cover.


📜 SIMILAR VOLUMES


Covers and Envelopes in Grothendieck Cat
✍ S.Tempest Aldrich; Edgar E Enochs; J.R Garcı́a Rozas; Luis Oyonarte 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 136 KB

In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of -covers and envelopes to the study of some properties of the class . We then prove the existence of flat covers and cotorsion envel

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✍ J. Rosický 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 97 KB

The flat cover conjecture, saying that every module has a flat (pre)cover, has been recently proved by Bican, El Bashir, and Enochs. We relate flat precovers (and cotorsion preenvelopes) to weak factorizations and prove that flat monomorphisms form a left part of a weak factorization system.

Brown representability and flat covers
✍ Henning Krause 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 66 KB

We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and at covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every add