We present a classification of those finite length modules X over a ring A that are isomorphic
to every module Y of the same length such that Ker (Hom A (−, X))= Ker (Hom A (−, Y)), that …

In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization
of the notion of both pure semisimple rings and of hereditary rings. Some properties and …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

In this note we prove that every Noetherian ring R of Krull dimension one has the PA-
property. Let us briefly recall the definition of the PA-property. Consider the foliowing data:(i) …

1. Introduction. Let R be a ring with unit element. R-mod is the category of left R-modules
and Sp (R-rood), the spectrum of R-rood, is the set of isomorphism classes of …

Modules in which every essential submodule contains an essential fully invariant
submodule are called endo-bounded. Let M be a nonzero module over an arbitrary ring R …

A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

Given a commutative ring A there are different approaches to understand its structure; one is
consider ideals and their arithmetic (multiplicative theory), and another one is to consider …

Colocalizing subcategories of DRfi Page 1 J. reine angew. Math. 653 (2011), 221—243 DOI
10.1515/CRELLE.2011.028 Journal fr die reine und angewandte Mathematik ( Walter de …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …