Using the concept of prime submodule defined by Raggi et al. in, for M∈ R-Mod we define
the concept of classical Krull dimension relative to a hereditary torsion theory τ∈ M-tors. We …

Page 1 NUMBER I77 T PH TO X /\!tal r" < - c: * Lu - -: *- < > KR Goodedr! and Ann K. Boyle
Dimension theory for nonsingular injective modules N/UEN/UOIRS OF THE AN/UERICAN N/UATHEN/UATICAL …

Let R be a commutative noetherian local ring. As an analog of the notion of the dimension of
a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of …

In this paper, we are interested in the following general question: Given a module M which
has finite hollow dimension and which has a finite collection of submodules K i (1≤ i≤ n) …

Recently Tachikawa[8] has proved that, if R is a ring of dominant dimension•† 1, then domi.
dim. RR•† 2 if and only if the injective hull E (RR) of RR has the double centralizer property …

Suppose that A is a semiprimary ring satisfying one of two conditions:(1) its Yoneda ring is
generated in finite degrees;(2) its Loewy length is less than or equal to three. We prove that …

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 …

We introduce and study the concept of essential Krull dimension as dual of small Krull
dimension of a module, which are defined in the same vein as Krull dimension of a module …

Let J be a directed set and let {Λj, φij} be a direct system of rings indexed by J and with limit
Λ. Let {Aj, φij} be a direct system of groups indexed by J. Assume that each Aj is a left Λj …

An R-module N is said to have finite width n if n is the smallest integer such that for any set of
n+ 1 elements of N, at least one of the elements is in the submodule generated by the …