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<p>Nada M. Al-Thani introduced pure closed submodules without adding any details about the behavior of this kind of submodule. The main goal of this paper is to study and develop pure closed submodules. We introduced several results that are analogous to those in the closed submodule. Besides that, we study pure closed submodules in multiplication modules. Also, the relationships of pure closed submodules with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_588_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(St\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">St</mi> </mrow> </math></EquationSource> </InlineEquation>-closed and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_588_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(W\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>W</mi> </math></EquationSource> </InlineEquation>-closed submodules are investigated. Moreover, ACC on pure closed submodules is discussed.</p>

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A study on pure closed submodules

  • 期刊论文

  • 发表日期：

    2025年4月5日

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  • Alaa Abdul Azeez Abdul Ameer,
  • Muna Abbas Ahmed

摘要

Nada M. Al-Thani introduced pure closed submodules without adding any details about the behavior of this kind of submodule. The main goal of this paper is to study and develop pure closed submodules. We introduced several results that are analogous to those in the closed submodule. Besides that, we study pure closed submodules in multiplication modules. Also, the relationships of pure closed submodules with \(St\) St -closed and \(W\) W -closed submodules are investigated. Moreover, ACC on pure closed submodules is discussed.