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 …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

The goal of this work is to develop a functional transfer of properties between a module A
and the category* M* E of right modules over its endomorphism ring* E that is more sensitive …

Introduction* The concept of the" injective envelope" of a module was first given by Eckmann
and Schopf [2], although this terminology was first employed by Matlis [5]. The injective …

1. Introduction. The injective hull E (M) of a module M is, by definition, a minimal injective
extension of. M. Here," minimal" can be taken to mean either that no intermediate module M …

It seems appropriate to first review the relevant properties of localization in comnutative
rings. Let R be a commutative ring (ail rings will be associative rings with identity element …