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 …

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 …

Let R be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …

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

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 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 small finitistic dimension of a ring is determined as the supremum projective dimensions
among modules with finite projective resolutions. This paper seeks to establish that, for a …

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 …

On modules which are flat over their is flat. Page 1 Hokkaido Mathematical Jour nal Vol. 7 (1978)
p. On modules which are flat over their endomorphism rings By Takeshi ONODERA (Received …

In this paper, we introduce the Krull dimension-dependent elements of a Noetherian
commutative ring. Let x, y be non-unit elements of a commutative ring R. x, y are called Krull …