The problem of classifying the torsion-free abelian groups with commutative endomorphism
rings appears as Fuchs' problems in [4, Problems 46 and 47]. They are far from solved, and …

The results of Szele and Szendrei ['On Abelian groups with commutative endomorphism
rings', Acta Math. Acad. Sci. Hungar. 2 (1951), 309–324] characterizing abelian groups with …

Let G be a torsion-free abelian group and let R be a commutative ring with 1. It is well known
[1] that if/~ is an integral domain then all units of the group ring RG are trivial, ie of the form r …

Since it was shown by Baer and Kaplansky that any isomorphism of the endomorphism rings
of primary abelian groups is induced by an isomorphism of the groups attention has been …

In [7] we studied torsion free abelian groups that are finitely generated as modules over their
endomorphism rings. It turns out that there is a surprisingly explicit and complete structure …

Let G and G* be abelian groups whose endomorphism rings E (G) and E (G*) are
isomorphic. There are few theorems in the literature giving circumstances under which …

Introduction. In [7] and [8] we have determined the isomorphisms of the endomorphism rings
of two special classes of torsion-free modules. In [7] the modules were free, over principal …

Publisher Summary This chapter describes a conjecture concerning the isomorphism
problem for commutative group algebras. Suppose R is a commutative ring with identity, and …

SEPARABLE ABELIAN GROUPS AS MODULES OVER THEIR ENDOMORPHISM RINGS
Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 91 …

1. Preliminaries. Abelian groups which are quasi-projective over their endomorphism rings
have been characterized by Fuchs in the torsion case. His methods have been extended by …