| Mohd Noman ALI,Vinit Kumar SHARMA,Ayazul HASAN.$QTAG$-Modules whose $h$-Pure-$S$-High Submodules Have Closure[J].数学研究及应用,2024,44(1):18~24 |
| $QTAG$-Modules whose $h$-Pure-$S$-High Submodules Have Closure |
| $QTAG$-Modules whose $h$-Pure-$S$-High Submodules Have Closure |
| 投稿时间：2023-03-14 修订日期：2023-09-22 |
| DOI：10.3770/j.issn:2095-2651.2024.01.003 |
| 中文关键词: $QTAG$-modules closures $h$-pure-$S$-high submodules |
| 英文关键词:$QTAG$-modules closures $h$-pure-$S$-high submodules |
| 基金项目: |
| 作者 | 单位 | | Mohd Noman ALI | Department of Mathematics, Shri Venkateshwara University, Gajraula, Amroha-U.P., India | | Vinit Kumar SHARMA | Department of Mathematics, Shri Venkateshwara University, Gajraula, Amroha-U.P., India | | Ayazul HASAN | College of Applied Industrial Technology, Jazan University, Jazan, Kingdom of Saudi Arabia |
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| 中文摘要: |
| A right module $M$ over an associative ring $R$ with unity is a $QTAG$-module if every finitely generated submodule of any homomorphic image of $M$ is a direct sum of uniserial modules. This article considers the closure of $h$-pure-$S$-high submodules of $QTAG$-modules. Here, we determine all submodules $S$ of a $QTAG$-module $M$ such that each closure of $h$-pure-$S$-high submodule of $M$ is $h$-pure-$\overline{S}$-high in $\overline{M}$. A few results of this theme give a comparison of some elementary properties of $h$-pure-$S$-high and $S$-high submodules. |
| 英文摘要: |
| A right module $M$ over an associative ring $R$ with unity is a $QTAG$-module if every finitely generated submodule of any homomorphic image of $M$ is a direct sum of uniserial modules. This article considers the closure of $h$-pure-$S$-high submodules of $QTAG$-modules. Here, we determine all submodules $S$ of a $QTAG$-module $M$ such that each closure of $h$-pure-$S$-high submodule of $M$ is $h$-pure-$\overline{S}$-high in $\overline{M}$. A few results of this theme give a comparison of some elementary properties of $h$-pure-$S$-high and $S$-high submodules. |
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