It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …

It is well known that a countably injective module is Σ-injective. In [KI Beidar, SK Jain, Ashish
K. Srivastava, New characterization of Σ-injective modules, Proc. Amer. Math. Soc. 316 …

Mathematical Journal of Okayama University Page 1 Mathematical Journal of Okayama
University Volume 51, Issue 1 2009 Article 6 A NOTE ON ALMOST INJECTIVE MODULES …

A pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest
possible, namely, consisting of exactly the absolutely pure modules. A module M is called …

A module is said to be extending, if every closed (ie complement) submodule is a direct
summand. This property is usually denoted by (Q). It is, obviously, equivalent to the …

It was shown in [5] that a finitely presented pure-injective module M has an indecomposable
decomposition if and only if M is completely pure-injective, that is, every pure quotient of M is …

In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

Pureinjective (or algebraically compact) modules have been studied extensively by many
authors (see [lo, 13, 14, 17, 191, for example). One of the main concerns of the theory is the …

Ž. It is well known that pure-injective s algebraically compact modules behave well in
relation to direct sum decompositions. Any indecomposable wx pure-injective module has …

The concept of a module M being almost N-injective, where N is some module, was
introduced by Baba (1989). For a given module M, the class of modules N, for which M is …