Abstract A right R-module N is called GP-flat if for any a∈ R, there exists a positive integer n
(depending on a) such that the sequence 0→ N⊗ Ran→ N⊗ R is exact. A left R-module M is …

Let R be a ring with Jacobson radical J (R). Following CNI, a submodule N of a left R-
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …

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

Let R be a ring, n, d be fixed non-negative integers, the class of (n, d)-injective left R-
modules, and the class of (n, d)-flat right R-modules. In this paper, we prove that if R is a left …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …

We prove that (a) if R is left coherent, then a finitely presented right R–module M is copure
flat if and only if M is a cokernel of a flat preen-velope (b) if R is a ring and na nonnegative …

PM Cohn [3] has introduced the notion of purity for R-modules. With respect to purity, flat,
absolutely pure and regular modules are studied. In this paper we introduce and study the …

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 m and n be fixed positive integers and M a right R-module. Recall that M is said to be (m,
n)-injective if for any (m, n)-presented right R-module P; M is called (m, n)-flat if for any (m, n) …

Let n≥ 1 be an integer. We introduce the notions of n-FP-gr-injective and n-gr-flat modules.
Then we investigate the properties of these modules by using the properties of special …