Author:
Hamad Amina T,Elewi Alaa A
Abstract
Abstract
Inthis paper, Z-Radical of module and Z-Lifting module and Z-local module are defined as ageneralization of radical of module and lifting module and local module. Where anR-module E has amaxima submodule define
R
a
d
(
E
)
=
∩
{
N
<
E
:
N
i
s
m
a
x
i
m
a
l
w
i
t
h
N
⊇
Z
2
(
E
)
}
z
. An R-module E iscalled Z-lifting if forany submodule N of E, there exists submodules X, H of E suchthat E = X⨁H with X ≤ N and N ∩ H «z
N. anR-module ग iscalled Z-local if
R
a
d
(
E
)
≪
z
E
z
and
R
a
d
(
E
)
z
is maximal. Several properties of these modules are proved.
Subject
General Physics and Astronomy