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<p>A module <i>C</i> is said to have the SIP when the intersection of any pair of direct summands of <i>C</i> is also a summand of <i>C</i>. In this manuscript, we define (strongly) summand intersection property on c-closed submodules, for short (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_601_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\({SSIP}^{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="italic">SSIP</mi> </mrow> <mi>c</mi> </msup> </math></EquationSource> </InlineEquation>) <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_601_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\({SIP}^{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="italic">SIP</mi> </mrow> <mi>c</mi> </msup> </math></EquationSource> </InlineEquation> if and only if the intersection of any pair of c-closed direct summands of <i>C</i> is (fully invariant) summand of <i>C</i>. Also, we introduced strongly CCLS if each c-closed submodule of <i>C</i> is a "fully invariant summand". We illustrate the structural features of these modules and locate these implications among some of modules’ properties.</p>

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Summand intersection property on c-closed submodules

  • 期刊论文

  • 发表日期：

    2025年6月30日

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  • Enas Mustafa Kamil

摘要

A module C is said to have the SIP when the intersection of any pair of direct summands of C is also a summand of C. In this manuscript, we define (strongly) summand intersection property on c-closed submodules, for short ( \({SSIP}^{c}\) SSIP c ) \({SIP}^{c}\) SIP c if and only if the intersection of any pair of c-closed direct summands of C is (fully invariant) summand of C. Also, we introduced strongly CCLS if each c-closed submodule of C is a "fully invariant summand". We illustrate the structural features of these modules and locate these implications among some of modules’ properties.