In this article, several characterizations of certain classes of rings via FC-purity and I-purity
are considered. Among others results, it is shown that every I-pure injective left R-module is …

This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …

Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this
paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this
paper is to study the class of commutative rings in which every S-flat module is flat (resp …

Let $ n, d $ be two non-negative integers. A left $ R $-module $ M $ is called $(n, d) $-
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A …

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

Let R be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …