We investigate conditions when the t-structure of Happel–Reiten–Smalø associated to a
torsion pair is a compactly generated t-structure. The concept of at CG torsion pair is …

For a left noetherian ring, we establish a bijective correspondence between equivalence
classes of cotilting-modules which are not necessarily finitely generated, and torsion pairs …

In this note we examine the 𝒯-torsion submodule of quasi-injective R-modules, R a ring with
unit, where 𝒯 is a torsion class in the sense of SE Dickson. We show that for a stable torsion …

Let τ be a hereditary torsion theory. The purpose of this paper is to extend results about
singular (resp. nonsingular) modules to τ-singular (resp. τ-nonsigular) modules. An R …

Let R be a ring with identity, and let M be a unitary (left) R-module. Then M is said to be
torsion provided that for every m∈ M, there is a nonzero r∈ R such that rm= 0. In this article …

Full article: An extension of S-artinian rings and modules to a hereditary torsion theory setting
Skip to Main Content Taylor and Francis Online homepage Taylor and Francis Online …

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 …

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 …

Let R be an associative ring with identity. An (left) R-module M is said to be torsion if for
every m∈ M, there exists a nonzero r∈ R such that rm= 0, and faithful provided rM={0} …

Injective and projective modules are studied relative to a hereditary torsion theory τ on Mod–
R. It is shown that every τ–projective module is projective if and only if the torsion ideal of R …