By using the concept of non-cosingularity, we introduced the class of γ \documentclass[12pt]{minimal}
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In this paper, we introduce the notion of FI-t-lifting modules which is a proper generalization
of both the concepts of t-lifting modules and FI-lifting modules. We show that a direct sum of …

A module M is called lifting if every submodule A of M contains a direct summand B of M
such that Bce,→ A in M. We call M is (strongly) FIlifting if every fully invariant submodule A of …

In this paper we introduce a new generalization of small submodules, namely γ-small
submodules. We call a submodule K of a module M, γ-small provided M= K+ L with M/L …

A module M is lifting if for every submodule A of M, there exists a direct summand B of M
such that B≤ A and A/B small in M/B. Every non-cosingular lifting module has the summand …

In this note we study the concept δ-lifting and we add some new results. Also we introduce
weak δ-lifting modules and FI-δ-lifting modules as two generalizations of δ-lifting modules …

In this paper, we introduce and study the concept of FI-hollow-lifting modules which is a
proper generalization of hollow-lifting modules. We say M called a fully invariant hollow …

Lifting modules as a main concept in module theory have been studied and investigated
extensively in recent decades. The first author in [1] tried to consider and investigate this …

In this paper we introduce the notions of $ G_ {1}^{*} L $-module and $ G_ {2}^{*} L $-
module which are two proper generalizations of $\delta $-lifting modules. We give some …

We introduce the concepts of lifting modules and (quasi‐) discrete modules relative to a
given left module. We also introduce the notion of SSRS‐modules. It is shown that (1) if M is …