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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 4, Pages 821-822

Quasi-projective modules and the finite exchange property

Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USA

Received 24 June 1987

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define a module M to be directly refinable if whenever M=A+B, there exists A¯A and B¯B such that M=A¯B¯ . Theorem. Let M be a quasi-projective module. Then M is directly refinable if and only if M has the finite exchange property.