An R-module M is said to be an extending module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of a type 2 τ-extending …

Torsion theories for abelian categories have been introduced in the 1960's with the
motivation and purpose of unifying a common behavior observed for abelian groups …

Let R be a commutative ring. An R-module M is called a semi-regular w-flat module if
\Tor_1^R(R/I,M) is \GV-torsion for any finitely generated semi-regular ideal I. In this article …

Let X be a class of left R-modules. It is proved that if type 2, t-extending Ieft-R-modules Mr
and M2 are relatively essentially. te-injective and Ml is pseudoly M2-X'-injective (or M2 is …

Notation and terminology concerning (hereditary) torsion theories on R-mod will follow [I]. In
particular, if T is a torsion theory on R-mod then a left ideal H of R is said to be T-dense in R …

Let M be a right R-module,\cal M the class of all M-small modules, and P a projective cover
of M in σ M. We consider the torsion theories\cal M=(\cal T _\cal M,\cal F _\cal M),\tau_V=(\cal …

In this paper, we give some characterizations of modules M over a ring R such that every
submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using …

Full article: Extension Closure of Relative k-Torsionfree Modules Skip to Main Content Taylor and
Francis Online homepage Taylor and Francis Online homepage Access provided by The …

Given a finite dimensional hereditary connected (basic-) algebra A of infinite representation
type the finite dimensional indecomposable modules divide into three classes: preprojective …