Covers, precovers, and purity

Henrik Holm; Jørgensen Peter

doi:10.1215/ijm/1248355359

Covers, precovers, and purity

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

62 Citationer (Scopus)

Abstract

We show that if a class of modules is closed under pure quotients, then it is precovering if and only if it is covering, and this happens if and only if it is closed under direct sums. This is inspired by a dual result by Rada and Saorín. We also show that if a class of modules contains the ground ring and is closed under extensions, direct sums, pure submodules, and pure quotients, then it forms the first half of a so-called perfect cotorsion pair as introduced by Salce; this is stronger than being covering. Some applications are given to concrete classes of modules such as kernels of homological functors and torsion free modules in a torsion pair.

Originalsprog	Engelsk
Tidsskrift	Illinois Journal of Mathematics
Vol/bind	52
Nummer	2
Sider (fra-til)	691-703
Antal sider	13
ISSN	0019-2082
DOI	https://doi.org/10.1215/ijm/1248355359
Status	Udgivet - 2008
Udgivet eksternt	Ja

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Covers, precovers, and purity

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