A CHARACTERIZATION OF GOLDIE EXTENDING MODULES OVER DEDEKIND DOMAINS

In this paper, we characterize G-extending (Goldie extending) modules over Dedekind domains and we use the G-extending condition to characterize the modules over a principal ideal domain whose pure submodules are direct summands. Moreover, we show that if R is a principal ideal domain, then the class of G-extending modules is closed under direct summands and that if R is a Dedekind domain, then the class of G-extending torsion modules is closed under finite direct sums.