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 …

Using definitions and properties by EE Enochs [1], VK Akatsa [2], EE Enochs and O. Mg
Jenda [3], we prove first, that, if (R α) α∈ I is a direct system of coherent rings, so that, for …

In this article, we introduce and study the concept of countably generated dimension, which
is a Krull-like dimension extension of the concept of DCC on countably generated …

Let R be a commutative unitary ring with X an analytic indeterminate. Unlike the situation for
polynomial rings, the weak global dimension of the power series ring R [[X]] need not be …

Following our previous work about quasi-projective dimension [11], in this paper, we
introduce quasi-injective dimension as a generalization of injective dimension. We recover …

In this paper we introduce and investigate M-cofaithful modules. A module N∈ σ M is called
M-cofaithful if for every 0≠ f∈ HomR (N, X) with X∈ σ M, Hom _R(X,M)f≠0. We show that if …

We define and studyco-Noetherian dimension of rings for which the injective envelopeof
simple modules have finite Krull-dimension. This is a Moritainvariant dimension that …

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 …

A ring R is called n-coherent if every (n− 1)-presented ideal of R is n-presented. In this
paper, the n-coherence of the perfect closure R∞ is investigated. We show that if R∞ is n …

In Section 1 of this paper, we investigate the finitely presented dimension of an essential
extension for a module, and obtain results concerning an essential extension of a torsion …