In this paper, we define and study a valuation dimension for commutative rings. The
valuation dimension is a measure of how far a commutative ring deviates from being …

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 …

R is called a right ${\Pi}-coherent $ ring in case every finitely generated torsion less right R-
module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi} …

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 …

INTRODUCTION In [3] and [l] the author developed the theory of dual Goldie dipsruion for
unitary left R-moduleo, where R is any ring with identity. Now, suppose R is a ring not …

Let M be a module which has finite uniform dimension and let K i (1≤ i≤ n) be a finite
collection of submodules of M such that 0= K 1∩···∩ K n. Then the uniform dimension u (M) …

Gabriel Dimension and Rings With Involution Page 1 HOUSTON JOURNAL OF
MATHEMATICS, Volume 4, No. 3, 1978. GABRIEL DIMENSION AND RINGS WITH …

All the rings and algebras considered in this paper will be commutative, with identity
elements and ring-homomorphisms will be unital. If A is a ring, then dim A will denote the …

In this paper, we study the dimension of a module over a commutative ring, which is defined
to be the length of a longest chain of prime submodules. This notion is analogous to the …

For any (S, R)-bimodule M, one can define an invariant d (M) by taking the supremum of n
for which there exists a direct sum of nonzero subbimodules N= M1⊕ M2⊕…⊕ Mn such …