<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2343</article-id>
      <title-group>
        <article-title>Purely-lifting modules</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Hamdi</surname>
            <given-names>Halah Qahtan</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Al-Mothafar</surname>
            <given-names>Nuhad S.</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>3</issue>
      <fpage>1355</fpage>
      <lpage>1363</lpage>
      <pub-date date-type="pub">
        <day>09</day>
        <month>03</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This article primary goal is to introduce the idea of purely lifting module, after that we proved  some properties of this concept the second aim is to studying  relations among purely lifting module and many others  module. The third aim is to introduce other notions such as cofinitely-purely-lifting modules and purely-hollow-lifting modules, as well as purely supplemented modules and H - purely supplemented modules.</p>
      </abstract>
      <kwd-group>
        <kwd>Lifting modules</kwd>
        <kwd>Pure sub-modules</kwd>
        <kwd>Purely-lifting modules</kwd>
        <kwd>Cofinitely -lifting modules</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
