Square-free modules with the exchange property

We prove that a square-free module with finite exchange has full exchange. More generally, if R is an exchange ring with R/J(R) Abelian. and R is endowed with a left linear. Hausdorff, Sigma-complete topology, then R is a full exchange ring. This provides an overarching framework for capturing many other results in the literature, such as the fact that quasi-continuous modules with finite exchange have full exchange. We further show that square-free modules with exchange satisfy an infinite version of the (C(3)) property. (C) 2010 Elsevier Inc. All rights reserved.