The idea of uniform modules was utilized to create what is now known as the uniform
dimension of a module (also known as the Goldie dimension). Some characteristics of the …

Let R be a ring with identity. Let C be a class of R-modules which is closed under
submodules and isomorphic images. Define a submodule C of an R-module M to be a C …

We define the presented dimensions for modules and rings to measure how far away a
module is from having an infinite finite presentation and develop ways to compute the …

In this paper, we are interested in the following general question: Given a module M which
has finite hollow dimension and which has a finite collection of submodules K i (1≤ i≤ n) …

M is called a dimension module if d (A+ B)= d (A)+ d (B)− d (A∩ B) holds for all submodules
A and B of M, where d (M) denotes the Goldie (uniform) dimension of a module M. We …

Introduction. Let R be a fixed (not necessarily commutative) ring. Throughout this nte, we are
concerned with left R-modules M, A, H, Like in'Goldie [1], we shall use the following …

In this paper, we introduce and study the concepts of non-essential Krull dimension and non-
essential Noetherian dimension of an R-module, where R is an arbitrary associative ring …

The formula dim (A+ B)= dim (A)+ dim (B)-dim (A∩ B) works when 'dim'stands for the
dimension of subspaces A, B of any vector space. In general, however, it does no longer …

In this paper, all rings are commutative with identity and all modules are unitary. Let R be a
ring and M an R-module. A proper submodule N of M is said to be prime (or P-prime) if rm …

Until now there has been no suitable dimension to measure how far a module deviates from
being uniserial. We define and study a new dimension, which we call uniserial dimension …