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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
Volume
1530
DOI
10.1088/1742-6596/1530/1/012070
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IRbHuIoBVTCNdQwC-aRI
ESSENTIAL T-hollow-lifting module
Sahira M. Yaseen
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Abstract<p>Let M be a R-module, where R be a commutative ring with identity, In this paper, we defined a new kind of module namely ET-hollow lifting module, Let T be a submodule of M, M is called ET-hollow lifting module if for every sub-module H of M with <inline-formula> <tex-math><?CDATA $\frac{M}{H}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mfrac> <mi>M</mi> <mi>H</mi> </mfrac> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> is <inline-formula> <tex-math><?CDATA $E(\frac{T+H}{H})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mfrac> <mrow> <mi>T</mi> <mo>+</mo> <mi>H</mi> </mrow> <mi>H</mi> </mfrac> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>-hollow, then there exists a direct summand D of M such that <inline-formula> <tex-math><?CDATA $D\subseteq E(\frac{T+D}{D})ce$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>D</mi> <mo>⊆</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mfrac> <mrow> <mi>T</mi> <mo>+</mo> <mi>D</mi> </mrow> <mi>D</mi> </mfrac> <mo stretchy="false">)</mo> <mi>c</mi> <mi>e</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012070_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula>. we introduce some properties of ET-hollow lifting module.</p>
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