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Communications in Algebra Volume 30, 2002 - Issue 6
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Original Articles

WHEN ARE PURE-INJECTIVE ENVELOPES OF FLAT MODULES FLAT?

Philipp Rothmaler Ohio State University, 435 Galvin Hall, 4240 Campus Drive, Lima, OH, 48504, U.S.A.
Pages 3077-3085 | Received 01 Jan 2001, Published online: 01 Sep 2006
 
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ABSTRACT

The question is answered in terms of flat covers, flat cotorsion modules, and cotorsion envelopes. It is shown that the corresponding class of rings properly contains that of coherent rings. The perfect rings among those are given a ring-theoretic description.

ACKNOWLEDGMENTS

I am grateful to Ed Enochs, Ivo Herzog, and the referee for valuable comments.

Notes

1Note the related result contained in Citation[5].

*For an independent treatment see Auslander M.; Smalo, S. O. Preprojective Modules over Artin Algebras, J. Algebra 1980, 66, 61–122.

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