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 …

Let m and n be fixed positive integers. R is called a right (m, n)-injective ring if every right R-
homomorphism from an n-generated submodule of the right R-module R m to R extends to …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

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 …

Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if
every n-generated submodule of M is finitely presented (resp. projective). We investigate the …

Recall that a ring R is said to be left coherent [2] if every finitely generated left ideal of R is
finitely presented. Coherent rings and their generalizations have been studied extensively …

A ring is called right P-coherent if every principal right ideal is finitely presented. Let MR be a
right R-module. We study the P-coherence of the endomorphism ring S of MR. It is shown …

Recently, Costa [4] introduced the concept of n-coherent rings. In this note we shall give
some further properties of n-coherent rings. Let R be a ring and na nonnegative integer …

Let R be a ring and U a left R-module with S= End (RU). The aim of this paper is to
characterize when S is coherent. We first show that a left R-module F is TU-flat if and only if …

Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp.
singly flat) if Ext1 (F/C, M)= 0 (resp. Tor1 (N, F/C)= 0) for any cyclic submodule C of any …