On generalizations of graded multiplication modules
| Autor: | Rashid Abu-Dawwas, Hicham Saber, Tariq Alraqad, Reem Jaradat |
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| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 40 (2022) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.51241 |
| Popis: | Let $G$ be a group with identity $e$, $R$ be a $G$-graded ring with unity $1$ and $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded quasi multiplication modules, where graded $M$ is said to be graded quasi multiplication if for every graded weakly prime $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. Also, we introduce the concept of graded absorbing multiplication modules; $M$ is said to be graded absorbing multiplication if $M$ has no graded $2$-absorbing $R$-submodules or for every graded $2$-absorbing $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. We prove many results concerning graded weakly prime submodules and graded $2$-absorbing submodules that will be useful in providing several properties of the two classes of graded quasi multiplication modules and graded absorbing multiplication modules. |
| Databáze: | Directory of Open Access Journals |
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