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 …

Anti-isomorphisms of the endomorphism rings of torsion-free modules Page 1 GEWIRTZMAN,
L. Math, Zeitschr. 98, 391--400 (1967) Anti-isomorphisms of the Endomorphism Rings of …

Let (R, M) denote the unitary left module M over the ring R, and let E (R, M) denote the ring
of all R endomorphisms of M. The purpose of this note is to show that the technique used by …

Motivated by the work of Baer [1], Kaplansky gave a proof in 1954 that any isomorphism of
the endomorphism algebras of two torsion modules over a complete discrete valuation …

Abstract A module RM is semiprime if for each 0≠ m ϵ M there exists ƒ ϵ Hom R (M, R) with
(mƒ) m≠ 0. In Section 1 semiprime artinian modules are seen to be isomorphic to finite …

In a fundamental paper [1], BAv.~ proved a number of definitive results concerning the
splitting off of the torsion subgroup of an abelian group. Not much has since been added to …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

In the initial sections of this paper we classify arbitrary torsion-free abelin groups in mnner
similar to that used to classify the subgroups of the ra-tionals. An existence theorem is …

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 …

1. Introduction. The concept of an «-local domain was introduced in [8, § 8] as a
simultaneous generalization of both a Dedekind domain and a local domain. It is a domain …