Assume that S is an almost excellent extension of R. Using functors Hom< sub> R(S,−) and—
⊗< sub> RS, we establish some connections between classes of modules [Figure not …

Let R be a ring, na fixed nonnegative integer and FP n (F n) the class of all left (right) R-
modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module …

In this paper we study cotorsion and torsion pairs induced by cotilting modules. We prove
the existence of a strong relationship between the Σ-pure-injectivity of the cotilting module …

Let R and S be arbitrary rings and let CSR be a semidualizing bimodule, and let 𝒜 C⁢(R op)
and ℬ C⁢(R) be the Auslander and Bass classes, respectively. Then both pairs (𝒜 C⁢(R …

Let R and S be rings and RCS a semidualizing bimodule, and let T be a subcategory of the
Auslander class AC (S) and H={C⊗ ST| T∈ T}. Then for any left R-module M, the T …

Let $ R $ be a ring, $ S $ a multiplicative subset of $ R $. An $ R $-module $ M $ is said to
be $ u $-$ S $-flat ($ u $-always abbreviates uniformly) if $\Tor^ R_1 (M, N) $ is $ u $-$ S …

In this article, we prove a similar theorem to C, Theorem 6 which holds in a more general
setting. In particular, we focus on the construction of a natural morphism giving rise to a …

Let R! A be a homomorphism of associative rings, and let. F; C/be a hereditary complete
cotorsion pair in R-Mod. Let. FA; CA/be the cotorsion pair in A-Mod in which FA is the class …

A duality between two categories C and 3) is an equivalence of categories between the dual
category Cop of C and 3). The idea of studying dualities between full subcategories of …

Let R and S be arbitrary associative rings. Given a bimodule, we denote by and the functors
and, where or S. We say that is a finitistic weakly cotilting bimodule (briefly FWC) if for each …