International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 4, Pages 821-822
doi:10.1155/S0161171289001018
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 Gary F. Birkenmeier. 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.
Abstract
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.