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 …

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 Nil∗(R) be the prime radical of R. In this paper, we say that a ring R is
left Nil∗-coherent if Nil∗(R) is coherent as a left R-module. The concept is introduced as the …

In this paper, we introduce a new generalization of coherent rings. Let m be a positive
integer and da positive integer or d=∞. A ring R is called a left (m, d)-coherent ring in case …

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 na fixed positive integer. A right R-module M is called strongly Jn-
injective if every R-homomorphism from an n-generated small submodule of a free right R …

This paper unifies several generalizations of coherent rings in one notion. Namely, we
introduce nX-coherent rings, where X is a class of modules and n is a positive integer, as …

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 …

On Π- coherence of rings Page 1 Hacettepe Journal of Mathematics and Statistics Volume
46 (5) (2017), 875 – 886 On Π- coherence of rings Zhu Zhanmin∗ Abstract Let n be a fixed …

In this note, we show that a ring $ R $ is $ S $-coherent if and only if every finitely presented
$ R $-module is $ S $-coherent, providing a positive answer to a question proposed in [D …