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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
Volume
1963
DOI
10.1088/1742-6596/1963/1/012029
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T-Small Quasi-Dedekind modules
Anfal Hasan Dheyab
Suad Naji Kadhim
Mukdad Qaess Hussain
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Abstract<p>Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if, <inline-formula> <tex-math><?CDATA $\forall \,w\,\in En{d}_{R}(Q),\,w\ne 0$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mo>∀</mo> <mspace width="0.25em"></mspace> <mi>w</mi> <mspace width="0.25em"></mspace> <mo>∈</mo> <mi>E</mi> <mi>n</mi> <msub> <mi>d</mi> <mi>R</mi> </msub> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="0.25em"></mspace> <mi>w</mi> <mo>≠</mo> <mn>0</mn> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1963_1_012029_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> then Ker w ≪<sub>T</sub> Q. Also, we illustrate it by examples and give basic properties.</p>
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