Let R be a commutative coherent ring and wD (R) denote the weak global dimension of R.
We prove that for an integer n≥ 2 the following are equivalent:.(a) wD (R) n;.(b) FP-idM⊗ …

In this paper, we study some properties of $ G_C $-flat $ R $-modules, where $ C $ is a
semidualizing module over a commutative ring $ R $ and we investigate the relation …

Let $ R $ be a ring, $ n $ a fixed non-negative integer, ${\mathscr {WI}} $ the class of all left $
R $-modules with weak injective dimension at most $ n $, and ${\mathscr {WF}} $ the class …

In this paper, with respect to a tilting module T, the notions of T< sub> M< sup> n-coherence
and T< sub> M< sup> n-flatness are introduced, for every module M and every nonnegative …

Let R be a ring and τ a hereditary torsion theory for the category of all left R-modules. A right
R-module M is called τ-flat if Tor 1 (M, R/I)= 0 for any τ-finitely presented left ideal I. A left R …

Let R be a ring and na fixed positive integer. A right R-module M is called strongly Jn-
injective if every R-homomorphism from an n-generated small submodule of a free right R …

Let $ R $ be a commutative ring. We first derive necessary and sufficient conditions for the
rings $ R\left\langle x\right\rangle $ and $ R (x) $ to be coherent. Next, for stably coherent …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …

In this article, we introduce and study the concepts of quasi-Krull dimension and quasi-
Noetherian dimension of an R-module, where R is an arbitrary associative ring. These …