In this article, we study modules with chain condition on non-finitely generated submodules.
We show that if an R-module M satisfies the ascending chain condition on non-finitely …

This article is a report of three lectures given on “Dimension Theory of Noetherian Rings”, at
the meeting “Infinite Length Modules”, held in Bielefeld, from 7th to 11th September 1998. I …

The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension
codim (End (MR)) of the endomorphism ring End (MR) of a module MR can be used as a …

IDEALS GENERATED BY THREE ELEMENTS idealI,d(R\l)=h. Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 35, No. 1, September 1972 IDEALS …

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 …

By defining orthogonal decomposition for modules, we prove that an R-module M has only
finitely many fully invariant direct summands if and only if End R (M) has triangulating …

In this note we consider the question: If R is a right Noetherian ring and I is an invertible
ideal of R, how do the Krull dimensions of various modules, factor rings and over-rings of R …

If R is left noetherian and M is a left R-module, then we can construct a complex called an
injective resolvent of M using injective precovers. Likewise, if R is left coherent and M is a …

Let R be a commutative coherent ring and wD (R) denote the weak global dimension of R.
We prove that for an integer n≥ 2 the following are equivalent:.(a) wD (R) n;.(b) FP-idM⊗ …

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 …