⊕-supplemented modules as a famous generalization of lifting (projective supplemented)
modules were widely studied in the last decades. In this paper, we peruse a homological …

Let R be a commutative ring with identity and all modules are unital. Various generalizations
of primary ideals and primary modules have been studied. For example, a proper ideal I of R …

Let R be a commutative ring with identity and M be an R-module. As a new generalization of
primary ideals to modules, a proper submodule N of M is a primary-like submodule if …

In this paper, we introduce principally⊕-supplemented modules as a generalization of⊕-
supplemented modules and principally lifting modules. This class of modules is a …

Let U be a submodule of a module M. We call U a strongly lifting submodule of M if
whenever M/U=(A+ U)/U⊕(B+ U)/U, then M= P⊕ Q such that P≤ A,(A+ U)/U=(P+ U)/U and …

Let R be a commutative ring with 1= 0, n be a positive integer and M be an R-module. In this
paper, we introduce the concept of n-absorbing primary submodules generalising n …

In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-
injective envelopes are studied. These modules will be called almost pure-injective …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

A right R-module N is called pseudo M-injective if for any submodule A of M, every
monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is …

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 …