In this paper we extend the notion of FP-injective modules to that of complexes and
characterize such complexes. We show that some characterizations similar to those for …

Let $ R $ be a commutative ring with $1\neq 0$ and $ n $ a positive integer. In this article,
we introduce the $ n $-Krull dimension of $ R $, denoted $\dim_n R $, which is the …

1. Introduction. Given the R-module A, we define the strong injective dimension and its dual
the strong projective dimension of A.(Our notations are Sid (A) and Spd (A) respectively.) …

Let R be a ring and let M be a left R-module. The classical Krull dimension of M was defined
to be the supremum of the lengths of all strong chains of prime submodules of M and …

Throughout this paper, R denotes a commutative ring and M an Artinian R-module. The
concept of Krull dimension for Artinian modules M was introduced first by RN Roberts in [10] …

It is well known that the right global dimension of a ring R is usually computed by the right
derived functors of Hom and the left projective resolutions of right R-modules. In this paper …

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 …

It is proven that the weak dimension of each FP-injective module over a chain ring which is
either Archimedean or not semicoherent is less or equal to 2. This implies that the projective …

It is known that if R is a right noetherian ring, then the corresponding Malcev-Neumann ring
R*((G)) is right noetherian and rK dim (R)= rK dim (R*((G))). We prove that the right noethe …

An ideal L of a ring R is said to be strongly hollow (briefly, sh-ideal) if L⊆ A+ B implies that
either L⊆ A or L⊆ B, for every pair A and B of ideals of R. We first, study and investigate …