The Jacobson radical of the endomorphism ring of a torsion-free abelian group

We study the action of elements of the Jacobson radical of the endomorphism ring of a torsion-free abelian group on the group itself.     

Quasiendomorphism algebras of some quasidecomposable rank 4 torsion-free abelian groups

We classify the quasiendomorphism algebras of rank 4 torsion-free abelian groups quasidecomposable as the direct sum of strongly indecomposable rank 2 groups.     

On the definability of completely decomposable torsion-free Abelian groups by endomorphism rings and some groups of homomorphisms

Mathematical Notes - In the present paper,we describe conditions on a vector group C which are necessary and sufficient for the class of completely decomposable torsion-free Abelian groups to be a...     

On the projective dimension of torsion-free abelian groups over the ring of its endomorphisms

Let E be the ring of endomorphisms of an abelian group G, and let the group G be given the structure of a left module over the ring E in the natural way. We solve the problem of determining the projective dimension of the module.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 117–124, January, 1970.     

The constructive theory of torsion-free abelian groups

The theory of torsion-free abelian groups is developed, in a manner that is constructive in the sense of Bishop, up to the fundamental the orem that, for finite-rank completely decomposable torsion-free groups, the class of finite-rank pure subgroups is coextensive with the class of finite-rank torsion-free quotients.     

Direct sums of local torsion-free abelian groups

The category of local torsion-free abelian groups of finite rank is known to have the cancellation and -th root properties but not the Krull-Schmidt property. It is shown that 10 is the least rank of a local torsion-free abelian group with two non-equivalent direct sum decompositions into indecomposable summands. This answers a question posed by M.C.R. Butler in the 1960's.

     

On endomorphism rings of primary abelian groups

Mathematische Annalen -     

Definability of separable torsion-free Abelian groups by endomorphism semigroups

In the class of separable torsion-free Abelian groups, we describe those which are defined by their endomorphism semigroups.Translated fromAlgebra i Logika, Vol. 34, No. 5, pp. 523–530, September-October, 1995.     

Separable pure subgroups of completely decomposable torsion-free abelian groups

Research partially supported by NSF grant no. DMS-8701074.