Finite rank torsion-free abelian groups uniserial over their endomorphism rings

Abstract

An abelian group is E E -uniserial if its lattice of fully invariant subgroups is totally ordered. Finite rank torsion-free reduced E E -uniserial groups are characterized. Such a group is a free module over the center C C of its endomorphism ring, and C C is a strongly indecomposable discrete valuation ring. Properties similar to those of strongly homogeneous groups are derived.