We show that a weak-injective module over an integral domain need not be pure-injective
(Theorem 2.3). Equivalently, a torsion-free Enochs-cotorsion module over an integral …

Over integral domains, we characterize modules of finite weak dimension⩽ n in terms of h-
divisible pure-injective modules (Theorems 2.1 and 2.2). We compare various classes of h …

We give a proof, based on the analysis of the divisible envelopes of flat modules, of the fact
that an integral domain R is almost perfect if and only if all divisible R-modules are weak …

Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …

1. This note is concerned primarily with a study of modules having zero singular submodule,
called torsion-free modules, over finitedimensional rings. In some of our results we do not …

In this paper we prove that a module M is invariant under automorphisms of its X-envelope if
and only if M is invariant under monomorphisms of its X-envelope where X is an enveloping …

We consider the problem of characterizing the commutative domains such that every module
admits a divisible envelope or a-cover, where is the class of modules of projective …

In this note, we provide a generalization of a well-known result of module theory which
states that two injective modules are isomorphic when they are isomorphic to submodules of …

1. Introduction. The notion of an injective cover has been recently introduced by Enochs r41
in terms of the dual of a categorical definition of an injective envelope. Earlier Enochs r31 …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …