A module is said to be copure injective if it is injective with respect to all modules A⊂ B with
B/A injective. We first characterize submodules that have the extension property with respect …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

Our concern is with modules M such that every homomorphism from a closed submodule of
M to M can be lifted to M. Although such modules share some of the properties of extending …

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 …

In this paper we study M-small principally injective (in short, M-sp-injective) module which is
the generalization of M-principally injective module. We prove that if M is finite dimensional …

The study of pure-injectivity is accessed from an alternative point of view. A module M is
called pure-subinjective relative to a module N if for every pure extension K of N, every …

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 …

We reprove that any injective module has a direct decomposition into a directly finite and a
purely infinite part ([8], Theorem 6), and we show that this decomposition has a strong …

New Characterization of σ-Injective Modules Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 136, Number 10, October 2008, Pages 3461-3466 S …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …