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 …

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 …

R denotes an associative ring with identity. Module means unitary right R-module. A module
has finite Goldie dimension over R if it does not contain an infinite direct sum of nonzero …

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 …

The concepts:'complement'and 'finite Goldie dimension'in the theory of modules (over rings)
are well known. The finite Goldie dimension of a submodule N of a module is usually …

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 …

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 …

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 …

Let Λ be a ring with unit. If A is a left Λ-module, the dimension of A (notation: 1. dimΛA) is
defined to be the least integer n for which there exists an exact sequence0→ Xn→…→ X0→ …

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.) …