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- W4376988419 abstract "Let $Gamma$ be a group, $Re$ be a $Gamma$-graded commutative ring with unity $1$ and $Im$ a graded $Re$-module. In this paper, we introduce the concept of graded weakly $J_{gr}$-semiprime submodules as a generalization of graded weakly semiprime submodules. We study several results concerning of graded weakly $J_{gr}$-semiprime submodules. For example, we give a characterization of graded weakly $J_{gr}$-semiprime submodules. Also, we find some relations between graded weakly $J_{gr}$-semiprime submodules and graded weakly semiprime submodules. In addition, the necessary and sufficient condition for graded submodules to be graded weakly $J_{gr}$-semiprime submodules are investigated. A proper graded submodule $U$ of $Im$ is said to be a graded weakly $J_{gr}$-semiprime submodule of $Im$ if whenever $r_{g}in h(Re),$ $m_{h}in h(Im)$ and $nin %TCIMACRO{U{2124} }% %BeginExpansion mathbb{Z} %EndExpansion ^{+}$ with $r_{g}^{n}m_{h}in U$, then $r_{g}m_{h}in U+J_{gr}(Im)$, where $J_{gr}(Im)$ is the graded Jacobson radical of $Im.$" @default.
- W4376988419 created "2023-05-18" @default.
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- W4376988419 date "2023-04-08" @default.
- W4376988419 modified "2023-09-30" @default.
- W4376988419 title "On graded weakly $J_{gr}$-semiprime submodules" @default.
- W4376988419 doi "https://doi.org/10.48550/arxiv.2305.08858" @default.
- W4376988419 hasPublicationYear "2023" @default.
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