On  Graded W-2-Absorbing Second Submodules: On Graded W-2-Absorbing Second Submodules

Thikrayat Alwardat; khaldoun Al-Zoubi

Authors

Thikrayat Alwardat Jordan University of Science and Technology
khaldoun Al-Zoubi Jordan University of Science and Technology

Keywords:

Graded W-2-Absorbing Second Submodules, Graded 2-Absorbing Second Submodules, Graded W-2-Absorbing Submodules

Abstract

Let $\Re$ be a commutative graded ring with unity, $\Im$ be a graded $\Re$-module,
$W$ be a multiplicatively closed subset of homogeneous elements of $\Re$ and $
K $ be a graded submodule of $\Im$ such that $Ann_\Re(K) \cap W = \emptyset $.
In this paper, we introduce the concept of graded $W$-2-absorbing second
submodules of $\Im$ as a generalization of graded 2-absorbing second
submodules. We say $K$ is a graded $W$-2-absorbing second submodule of $\Im$,
if there exists a fixed $s_\alpha \in W$ and whenever $r_g t_h K \subseteq H$%
, where $r_g, t_h \in h(\Re)$ and $H$ is graded submodule of $\Im$, then either $
s_\alpha r_g K \subseteq H$ or $s_\alpha t_h K \subseteq H$ or $s_\alpha r_g
t_h \in Ann_\Re(K) $. Several results concerning these classes of graded
submodules are given.

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On Graded W-2-Absorbing Second Submodules