Let
G
G
be an abelian group with identity
e
e
. Let
R
R
be a
G
G
-graded commutative ring and
M
M
a graded
R
R
-module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components. Special attention has been paid, when graded rings are graded gr-Noetherian, to find extra properties of these graded submodules.
Let G be a group with identity e. Let R be a G-graded commutative ring with
identity and M a graded R-module. We introduce the concept of graded
Ie-prime submodule as a generalization of a graded prime submodule for I
=?g?G Ig a fixed graded ideal of R. We give a number of results concerning
this class of graded submodules and their homogeneous components. A proper
graded submodule N of M is said to be a graded Ie-prime submodule of M if
whenever rg ? h(R) and mh ? h(M) with rgmh ? N ? IeN, then either rg ? (N :R
M) or mh ? N.
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In this paper, we introduce the concepts of graded G2-absorbing and graded strongly G2-absorbing second submodules of graded modules over graded commutative rings. We give a number of results concerning these classes of graded submodules and their homogeneous components.
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