Lifting Projectives
- 1 July 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 27 (2) , 747-751
- https://doi.org/10.1017/s0027763000026520
Abstract
Let R be a ring with radical (all rings have a unit element, all modules are unital). Often, one wishes to lift modules modulo , that is, to a given, say, left R/-module U find a left R-module E with the property that E/E ≃ U. This is of course not always possible. Here I prove, roughly, that if a finitely generated projective U can be lifted at all, it can be lifted to a projective. Or rather, if U can be lifted to an E satisfying a certain mild condition, then E is projective (Lemma).Keywords
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