This note shows that if T is a commutative ring with prime subring R, then all subrings of T
have Krull dimension at most m if and only if the supremum over all minimal prime ideals of …

Two modules are said to be orthogonal if they do not have nonzero isomorphic submodules.
An atomic module is any nonzero module whose nonzero submodules are not orthogonal. A …

Dimension of a ring with respect to a subring Page 1 Journal of Algebra and Its Applications Vol.
19, No. 11 (2020) 2050215 (15 pages) c© World Scientific Publishing Company DOI …

On the primary-like dimension of modules Page 557 ITALIAN JOURNAL OF PURE AND
APPLIED MATHEMATICS–N. 49–2023 (538–548) 538 On the primary-like dimension of …

Let, ℬ be classes of modules, we introduce and characterize orthogonal dimensions of
modules and rings by the orthogonal classes of modules⊥,⊥ ℬ, and T. For an almost …

We investigate injective dimension of $ F $-finite $ F $-modules in characteristic $ p $ and
holonomic $ D $-modules in characteristic 0. One of our main results is the following. If …

We present some methods for calculating the module's uniserial dimension that finitely g
enerated o ver a DVD in this article. The idea of a module's uniserial dimension over a …

We introduce and study the concept of dual perfect dimension which is a Krull-like
dimension extension of the concept of acc on finitely generated submodules. We observe …

Let C be a given class of mathematical objects and assume that for any X£ C a certain
“dimension” 8 (X), which is an ordinal number or oo, was defined. Then, it is very natural to …

In recent works by Eilenberg Nagao and Nakayama [# I, Jans and Nakayama [8], Harada [7],
and Zaks [II] the problem of characterizing semi-primary rings all of whose residue rings …