ESSENTIAL T-hollow-lifting module

Sahira M. Yaseen

doi:10.1088/1742-6596/1530/1/012070

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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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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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Publication Date

Thu Mar 03 2022

Journal Name

Archives Of Rheumatology

Association of tumor necrosis factor-alpha promoter region gene polymorphism at positions -308G/A, -857C/T, and -863C/A with etanercept response in Iraqi rheumatoid arthritis patients

Samer Imad

Munaf

Faiq

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Objectives: This study aims to evaluate the association between polymorphisms in the promoter region of the tumor necrosis factor-alpha (TNF-α) gene at locations -308G/A, -857C/T, and -863C/A with the tendency of being non-responder to etanercept.

Patients and methods: Between October 2020 and August 2021, a total of 80 patients (10 males, 70 females; mean age: 50 years; range, 30 to 72 years) with rheumatoid arthritis (RA) receiving etanercept for at least six months were included. The patients were divided into two groups responders and non-responders, based on their response after six months of continuous treatment. Following polymerase chain reac

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Publication Date

Mon Jan 02 2023

Journal Name

Pakistan Heart Jornal

The Effect of the Strategy of Differentiated Education According to the Auditory Learning Style by Using Assistance in Learning the Back Kick (T-Chagi) for the Young Players of …

Ban Adnan

Ahmed Hadi

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Publication Date

Wed Dec 30 2015

Journal Name

College Of Islamic Sciences

Achieve breastfeeding book and theft book To the end of the door cut the way of the manuscript Sailing Forum for Sheikh Ibrahim bin Mohammed Halabi (T: 659 H): Study and achieve

أ.م.د. قصي سعيد

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Achieve breastfeeding book and theft book
To the end of the door cut the way of the manuscript
Sailing Forum for Sheikh Ibrahim bin Mohammed Halabi
(T: 659 H)

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