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 Ext1 (P, M)= 0 for any (m, n)-presented right R-module P; M is said to be (m, n) …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

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. 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 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 …

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 M be a module. A\delta-cover of M is an epimorphism from a module F onto M with
a\delta-small kernel. A\delta-cover is said to be a flat\delta-cover in case F is a flat module. In …

Let R be a ring, na fixed non-negative integer and ℱ the class of all left R-modules of FP-
injective dimensions at most n. It is proved that all left R-modules over a left coherent ring R …

We introduce nets in rings, which turn out to describe right flat modules and left flat modules
over a fixed ring R at the same time. As an application we prove that for a finitely generated …