Abstract Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of
rings and modules. They provide useful technical tools for studying their structure. We define …

It is known that a ring R is left Noetherian if and only if every left R-module has an injective
(pre) cover. We show that (1) if R is a right n-coherent ring, then every right R-module has an …

IDEALS GENERATED BY THREE ELEMENTS idealI,d(R\l)=h. Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 35, No. 1, September 1972 IDEALS …

In this paper, we introduce the notion of Wn-modules and describe non-commutative
coherent rings with finite FP-selfinjective dimension. The obtained results generalize the …

In this article, we introduce the concept of parallel Krull dimension of a module (briefly, p.
Krull dimension), which is Krull-like dimension extension of the concept of DCC on poset of …

In this paper, we introduce the concept of nonnil-FP-injective dimension for both modules
and rings. We explore the characterization of strongly ϕ-rings that have a nonnil-FP-injective …

We investigate injective dimension of $ F $-finite $ F $-modules in characteristic $ p $ and
holonomic $ D $-modules in characteristic 0. One of our main results is the following. If …

Let R be a commutative ring with identity and let (X,)", be a set of indeterminates over R. It is
well known that if R is a Noetherian ring, then dim RIX,)",]= dim R|| X,)",|= dim RIm. In this …

The concepts of Ding projective, injective R-modules were first introduced by Ding and his
partners in [J. Aust. Math. Soc., 86 (2009), 323–338] and [J. Algebra Appl., 7 (4)(2008), 491 …

Let R be a ring with an identity and, for a left Λ-module RM, pd (M) and ίd (M) denote the
projective and injective dimension of RM, respectively. A (left and right) noether ring R is …