In this paper, by taking the class of all C 3 (or D 3) right R-modules for general envelopes
and covers, we characterize a semisimple artinian ring (or a right perfect ring) via D 3-covers …

In this paper, we characterize strongly right C 2-rings in terms of finite-direct-injective
modules which is a generalization of direct-injective modules (or C 2-modules). Using this …

The notion of simple-direct-injective modules which are a generalization of injective
modules unifies $ C2 $ and $ C3 $-modules. In the present paper, we introduce the notion of …

Given an R-module C and a class of R-modules 𝒟 over a commutative ring R, we investigate
the relationship between the existence of 𝒟-envelopes (respectively, 𝒟-covers) and the …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

In Bican et al., it is proved that all modules over an arbitrary ring have flat covers. In this
article, we shall study rings over which flat covers of finitely generated modules are …

Carl Faith in 2003 introduced and investigated an interesting class of rings over which every
cyclic right module has Σ-injective injective hull (abbr., right CSI-rings). Inspired by this we …

In this article, we characterize some rings in terms of the DG-projective, injective and flat
complexes. We also give some connections between DG-injective complexes and DG-flat …

Following, a ring R is called right almost-perfect if every flat right R-module is projective
relative to R. In this article, we continue the study of these rings and will find some new …

In this paper, we investigate the notions of X⊥‐projective, X‐injective, and X‐flat modules
and give some characterizations of these modules, where X is a class of left modules. We …