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Lifting Projectives

Published online by Cambridge University Press:  22 January 2016

Jan R. Strooker
Jan R. Strooker*
Affiliation:
University of Utrecht
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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).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 747 - 751
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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