### Fully Invariant M-Lifting Modules

*Yahya Talebi*

#### Abstract

Let M be any preradical for [M] and N any module in [M]. A

module N is called M-lifting if for every submodule K of N, there is

a decomposition K = A B, such that A is a direct summand of N

and B M(N). We call N is (strongly) FI-M-lifting if for every fully

invariant submodule K of N, there is a decomposition K = AB, such

that A is a (fully invariant) direct summand of N and B M(N). The

class of FI-M-lifting modules properly contains the class of M-lifting

modules and the class of strongly FI-M-lifting modules. In this paper

we investigate whether the class of (strongly) FI-M-lifting modules are

closed under particular class of submodules, direct summands and direct

sums.

module N is called M-lifting if for every submodule K of N, there is

a decomposition K = A B, such that A is a direct summand of N

and B M(N). We call N is (strongly) FI-M-lifting if for every fully

invariant submodule K of N, there is a decomposition K = AB, such

that A is a (fully invariant) direct summand of N and B M(N). The

class of FI-M-lifting modules properly contains the class of M-lifting

modules and the class of strongly FI-M-lifting modules. In this paper

we investigate whether the class of (strongly) FI-M-lifting modules are

closed under particular class of submodules, direct summands and direct

sums.

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