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 …

We define a dimension, called the finitely presented dimension, for modules and
commutative rings. This dimension has nice properties when the ring in question is …

In this article, we introduce and study a generalization of the classical Krull dimension for a
module MR. This is defined to be the length of the longest strong chain of prime submodules …

Let R be a ring with identity and M a unital right R-module. By the finite Goldie dimension of
M is meant the largest integer m (provided it exists) such that M contains the direct sum of m …

The main result of this note is that a semiprime ring with Krull dimension is a right order in a
semisimple artinian ring. In [3] this theorem is cast in the more general context of rings with …

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree
dimension of finitely generated R-modules. For any n≧0, we prove that R is a Gorenstein …

On the Finiteness of the Global Dimension for Artinian Rings Page 1 Journal of Algebra 251,
475–478 (2002) doi:10.1006/jabr.2001.9130 On the Finiteness of the Global Dimension for …

If $ R $ is a Noetherian ring and $ n $ is a positive integer, then there are only finitely many
ideals $ I $ of $ R $ such that the residue class ring $ R/I $ has cardinality $\leq n $. If $ R …

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 …

INTRODUCTION. The main results of this paper show that homological dimensions over a
fully bounded noetherian (FBN) ring R may be computed using just simple R-modules, as …