If M denotes the class of unitary left modules over a ring R, then each subclass# ofM
determines two subclasses ofJt—the relative projectivity class and the relative injectivity …

Kaplansky proved in [3, Theorem 2] that over a local 1 ring any projective module is free.
Another large class of projective modules were shown to be free a few years later. Bass [2 …

The purpose of this paper is to study further the ideal and module structure of a commutative
ring with identity, in which every principal ideal is projective. Results concerning particular …

Let ${P_R} $ be a projective module with trace ideal $ T $. An $ R $-module ${X_R} $ is $ T
$-accessible if $ XT= X.{\text {If}}{P_R} $ is finitely generated projective and $ C $ is the $ R …

It is shown that if $ M $ is a finitely presented completely pure injective object in a locally
finitely generated Grothendieck category ${\mathbf {C}} $ such that $ S={\operatorname …

The homological classification of rings is based on the length of projective resolutions of
modules, but it tells us nothing about the projective modules themselves. For information on …

We prove that every∑-pure-injective module over a serial ring is serial and every∑-pure-
injective faithful indecomposable module over a serial ring is∑-injective. Moreover, every …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

ANY finitely generated Abelian group A is a finite direct sum of cyclic groups. Gathering
together the infinite cyclic direct summands in this decomposition of A it follows that A= B© …