Let R be a ring and n be a positive integer. R is called left n-coherent, if every n-presented
left R-module is (n+ 1)(n+ 1)-presented. A left R-module M is called (n, 0)-injective if Ext …

A module MR is called FCG-projective if Ext R 1 (M, A)= 0 for every finitely cogenerated right
R-module A. A ring R is called right co-hereditary if every factor module of a finitely …

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 M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of
S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator ann M n …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

Let R be a ring and m, n two fixed positive integers. In this article, R is defined to be left
slightly (m, n)-coherent if each n-generated submodule of the left R-module Rm is (m, n) …

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 …

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, and n and d fixed non-negative integers. An R-module M is called (n, d)-
injective if Ext d+ 1 R (P, M)= 0 for any n-presented R-module P. M is said to be (n, d) …