A characterization of Goldie extending modules over Dedekind domains

OpenAlex İngilizce

In this paper, we characterize [Formula: see text]-extending (Goldie extending) modules over Dedekind domains and we use the [Formula: see text]-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 [Formula: see text]-extending modules is closed under direct summands and that if R is a Dedekind domain, then the class of [Formula: see text]-extending torsion modules is closed under finite direct sums.