Throughout this paper it is assumed that rings are associative, have the identity element,
and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R …

I. Introduction. Irving Kaplansky observed that, for a free module over a principal ideal
domain, the intersection of any two direct summands is again a direct summand [K]. Problem …

EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS Page 1 Canad. Math.
Bull. Vol. 16 (4), 1973 EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS BY …

Y. Utumi obtainedthat ifa ring R is left self-injective then so is the residue class ring R/J
modulo the Jacobsn radical J of R. And BL Osofsky [5] extended this result to the case of …

Hans Zassenhaus has recently shown [4] that a torsion-free (associative) ring E with identity,
whose additive group E+ is free and of finite rank, can be represented as the endomorphism …

Throughout this paper R will be a commutative ring with one, and all R-modules will be
unitary. Our purpose is to study commutative ring exten-sions S of R. As a key tool in our …

In this paper we study the endomorphism rings of certain separable torsion-free abelian
groups where, following Baer [1], an abelian group is separable if every finite subset of the …

Let 8%'denote the category of torsion-free J?-modules of finite rank with morphism sets K®
RHomR (A, B), where R is a discrete valuation ring with unique maximal ideal (p), K is the …

We shall consider here only commutative Noetherian rings with unit, and all modules are to
be taken as left unitary modules. In his paper [2], Matlis defined for a module A over a …