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 $ 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 …

In 2010, Sanh et al. introduced a class of pseudo-M-gp-injective modules, following this, a
right R-module N is called pseudo-M-gp-injective if for any homomorphism 0= α∈ End (M) …

Abstract A left R-module M is said to be fp-injective if, for every monomorphism K→ L with K
and L finitely presented left R-modules, Hom (L, M)→ Hom (K, M) is an epimorphism. A right …

Let R be a commutative ring with a nonzero identity and M an R-module. Set ϕ-tor (M)={x∈
M| sx= 0 for some s∈ R∖ Nil (R)}, if ϕ-tor (M)= M then M is called a ϕ-torsion module. An R …

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 …

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 …

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 …

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 …

Let $ R $ be a commutative ring with nonzero identity. An $ R $-module $ M $ is called $\phi
$-P-flat if $ x\in\Ann (s) M $ for every non-nilpotent element $ s\in R $ and $ x\in M $ such …