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 …

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 …

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 …

Let R be a ring. Recall that a left R-module M is coherent if every finitely generated
submodule of M is finitely presented. R is a left coherent ring if the left R-module RR is …

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 …

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 …

Recently, Xiang and Ouyang defined a (commutative unital) ring R to be Nil*-coherent if
each finitely generated ideal of R that is contained in Nil (R) is a finitely presented R-module …

Let R be a commutative ring with 1 ≠ 0 1≠ 0 and let H={R| R\; is\; a\; commutative\; ring\;
and\; Nil (R)\; is\; a\; divided\; prime ideal\; of\; R\} H= R| R isacommutativeringand N il (R) …

Let R be a commutative ring. If the nilpotent radical N il (R) of R is a divided prime ideal, then
R is called a ϕ-ring. In this paper, we first distinguish the classes of nonnil-coherent rings …

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 …