ABSTRACT
Throughout, all rings considered are commutative with unity. Recall that a module is uniserial if its lattice of submodules forms a chain. Let R be a ring and A an R-module. We shall use Soc(A) to denote the socle of A and U(A) to denote the sum of all uniserial submodules of A. If G is an abelian group, U(G) coincides with the torsion part of G.
