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 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, 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 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 …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

Let R be a strong n-coherent ring such that each finitely n-presented R-module has finite
projective dimension. We consider ℱ 𝒫 n (R) the full subcategory of R-Mod of finitely n …

Let n≥ 1 be an integer. We introduce the notions of n-FP-gr-injective and n-gr-flat modules.
Then we investigate the properties of these modules by using the properties of special …

In this paper, we introduce the notion of “P-coherent rings” which is a generalization of the
notion of “coherent rings”. Then we establish the transfer of this notion to pullbacks, direct …

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 …