The exchange property of modules with the finite exchange property - Dhompongsa S. (2014)
The question, posed in Crawley and Jónsson (Crawley, P., Jónsson, B. (1964). Refinements for infinite direct decompositions of algebraic systems. Pacific J. Math. 14:797-855.), whether the finite exchange property implies the unrestricted exchange property for any modules, is still open. In this note we obtain the equivalence of the finite exchange property and the unrestricted exchange property for the class of modules whose endomorphism rings are Abelian.