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 …

Every Abelian group can be related to an associative ring with an identity element, the ring
of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has …

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

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 …

A COMBINATORIAL THEOREM AND ENDOMORPHISM RINGS OF ABELIAN GROUPS II §0
Introduction Saharon Shelah (*) University of Jerusalem Page 1 A COMBINATORIAL …

It is shown that if the full ring R= E (G) of all endomorphisms of an abelian group G is left self-
injective, then G= D⊕ H, D torsionfree divisible and H is a pure fully invariant subgroup of∏ …

1. Introduction. Sometimes, a general theorem for a class of abelian groups can be proved
by first showing that the property lives in the en-domorphism rings. Then some theorems are …

The paper contains Parts 1, 2, 3, and 4 of a review of the authors on endomorphism rings of
Abelian groups. Most of the results are given with proofs. Part 1 contains some general …

As the title indicates, we are concerned in this paper with abelian groups that are projective
as modules over their endomorphism rings. We will in fact limit our attention to those groups …

Let G be a mixed abelian group and let R= E (G) denote the endomorphism ring of G. This
paper investigates the problem: under which conditions is the ring R is a von Neumann …