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 …

In [9], the author extends the definition of lifting and supplemented modules to?-lifting and?-
supplemented by replacing" small submodule" with"?-small submodule" introduced by Zhou …

Let $ M $ be a left module over a ring $ R $ and $ I $ an ideal of $ R $. $ M $ is called an $ I
$-supplemented module (finitely $ I $-supplemented module) if for every submodule (finitely …

In this article, we consider the module theoretic version of I-semiperfect rings R for an ideal I
which are defined by Yousif and Zhou. Let M be a left module over a ring R, N∊ σ [M], and τ …

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous of δ-supplemented modules defined by Kosan. The …

Let M be a left module over a ring R and I an ideal of R. M is called an I-supplemented
module (finitely I-supplemented module) if for every submodule (finitely generated …

Abstract Motivated by [1], we study on\tau-lifting modules (rings) and\tau-semiperfect
modules (rings) for a preradical\tau and give some equivalent conditions. We prove that; i) if …

In this work, we prove that an R-module M is cofinitely δ-supplemented (ie each cofinite
submodule of M has a δ-supplement) if and only if every maximal submodule of M has a δ …

ABSTRACT A submodule N of a module M is δ-small in M if N+ X≠ M for any proper
submodule X of M with M∕ X singular. A projective δ-cover of a module M is a projective …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …