ON GRADED S-PRIME SUBMODULES OF GRADED MODULES OVER GRADED COMMUTATIVE RINGS
2021 ◽
Vol 10
(11)
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pp. 3479-3489
Keyword(s):
Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity, $M$ a graded $R$-module and $S\subseteq h(R)$ a multiplicatively closed subset of $R$. In this paper, we introduce the concept of graded $S$-prime submodules of graded modules over graded commutative rings. We investigate some properties of this class of graded submodules and their homogeneous components. Let $N$ be a graded submodule of $M$ such that $(N:_{R}M)\cap S=\emptyset $. We say that $N$ is \textit{a graded }$S$\textit{-prime submodule of }$M$ if there exists $s_{g}\in S$ and whenever $a_{h}m_{i}\in N,$ then either $s_{g}a_{h}\in (N:_{R}M)$ or $s_{g}m_{i}\in N$ for each $a_{h}\in h(R) $ and $m_{i}\in h(M).$
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2015 ◽
Vol 08
(02)
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pp. 1550016
2017 ◽
Vol 37
(1)
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pp. 153-168
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2009 ◽
Vol 52
(2)
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pp. 253-259
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2019 ◽
Vol 32
(2)
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pp. 103
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2001 ◽
Vol 43
(1)
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pp. 103-111
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Keyword(s):
1977 ◽
Vol 18
(1)
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pp. 101-104
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