ABSTRACT
Let R be an integral domain with quotient field Q. An J?-module G is torsionrx = 0 implies ~ = 0 or x = 0 whenever r € R and x € G. The rank of
a torsion-free module G is the size of a-maximal linearly independent subset of G, from which it follows that X is torsion-free of rank 1 if and only if X is isomorphic to a submodule of Q. A finite rank completely decomposable module is a finite direct sum of rank 1 modules.
