Open Access
Summer 2008 Covers, precovers, and purity
Henrik Holm, Peter Jørgensen
Illinois J. Math. 52(2): 691-703 (Summer 2008). DOI: 10.1215/ijm/1248355359


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.


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Henrik Holm. Peter Jørgensen. "Covers, precovers, and purity." Illinois J. Math. 52 (2) 691 - 703, Summer 2008.


Published: Summer 2008
First available in Project Euclid: 23 July 2009

zbMATH: 1189.16007
MathSciNet: MR2524661
Digital Object Identifier: 10.1215/ijm/1248355359

Primary: 16E30 , 18G25

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

Vol.52 • No. 2 • Summer 2008
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