In this article, FP-injective complexes are introduced and studied. We prove that (⊥ ℱℐ, ℱℐ)
is a hereditary cotorsion theory if and only if R is a left coherent ring, where ℱℐ denotes the …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

We prove that every perfect torsion theory for a ring R is differential (in the sense of [PE
Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1–8]). In …

The aim of this paper is to unify classification theories of torsion classes of finite dimensional
algebras and commutative Noetherian rings. For a commutative Noetherian ring R and a …

Let R be a complete discrete valuation ring (possibly non-commutative). If K is the quotient
field of R then there is an isomorphism between the category of divisible torsion R-modules …

Let A and B be two rings, M be a left B, right A bimodule and be the formal triangular matrix
ring. It is known that the category of right T-modules is equivalent to the category Ω of triples …

The concept of cotorsion was first introduced in the category of Abelian groups (Fuchs [l]).
Matlis [5], studied the cotorsion modules over integral domains. Henderson and Orzech [4] …

Let τ be an hereditary torsion theory. For a ring with τ-Gabriel dimension, we find necessary
and sufficient conditions for the existence of a bijective correspondence between the τ …

1. Introduction. Let R be a ring with unit element. In [4] J. Golan has introduced the notion of
semi-stable torsion theory. A torsion theory 7 i, s called semi-stable if, every indecomposable …

A well-known theorem of Hopkins and Levitzki states that any left artinian ring with identity
element is left noetherian. The main theorem of this paper generalizes this to the situation of …