Modules in which every essential submodule contains an essential fully invariant
submodule are called endo-bounded. Let M be a nonzero module over an arbitrary ring R …

Let R be a noetherian ring and S an excellent extension of R. cid (M) denotes the copure
injective dimension of M and cfd (M) denotes the copure flat dimension of M. We prove that if …

In this paper, we introduce the concept of nonnil-FP-injective dimension for both modules
and rings. We explore the characterization of strongly ϕ-rings that have a nonnil-FP-injective …

We prove that (a) if R is a left coherent ring, then the weak global dimension w D (R)<= n
(n>= 2) if and only if every (n–2) th F–cosyzygy of a finitely presented right R–module has a …

This is a study of Ding projective modules relative to a semidualizing module and related
topics. Firstly, we study DC-projective dimensions and DC-projective modules under change …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

For a hereditary torsion theory T, this paper mainly discuss properties of A-τ-injective
modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a …

In this paper, we first introduce and study the notions of strongly $\phi $-flat modules and
strongly nonnil-injective modules. And then, we investigate the homology dimensions of …

Let $ R $ be a commutative ring with identity and $ S $ a multiplicative subset of $ R $. First,
we introduce and study the $ u $-$ S $-projective dimension and $ u $-$ S $-injective …