We derive a necessary and sufficient condition that an isomorphism between the
endomorphism rings of modules be induced by a semi-linear isomorphism of the modules …

Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

Let R be a ring and M a right R-module. Let σ [M] be the full subcategory of Mod-R
subgenerated by M. An M-natural class 𝒦 is a subclass of σ [M] closed under submodules …

We establish equivalent conditions under which every object in an Abelian category has a
monic X-cover and an epic X-envelope respectively, when X is a class of objects closed …

Let R be any ring with identity. We show that the homotopy category of all acyclic chain
complexes of pure-projective R-modules is a compactly generated triangulated category …

1. Introduction. In this paper we will construct a functor G: M--, G (M) from the category of
torsion-free modules M to the category of mixed modules G (M). As we will see below, the …

This paper describes properties of three certain classes of modules M over a ring R
determined by conditions on isomorphic direct summands (≲⊕): The condition that …

Let 0—X→ Y→ Z–0 be an almost split sequence in the category of R-modules and suppose
Z is finitely presented. A modeltheoretic characterization of X in terms of Z is given, as well …

Publisher Summary This chapter discusses flatness and projectivity of modules that come
from ℂ-sets. The chapter presents a case where M is a ℂ-set. If nonadditive flatness and …

This review paper is concerned with modules in which all automorphisms (endomorphisms)
of submodules can be extended to endomorphisms of the entire module. We consider old …