ESSENTIAL T-hollow-lifting module
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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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