<?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-2271</article-id>
      <title-group>
        <article-title>Small 2-prime sub-modules</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Hassan</surname>
            <given-names>Huda Ali</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Elewi</surname>
            <given-names>Alaa A.</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>4-B</issue>
      <fpage>1331</fpage>
      <lpage>1336</lpage>
      <pub-date date-type="pub">
        <day>26</day>
        <month>06</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>For an D-module (abbreviated D-mod) W and a commutative ring (with identity) D. we introduce the notion of small 2-prime sub-module (S-2-P sub-module; for short ) as a generalization of 2-prime sub-module. We prove many properties for this kind of sub-modules, among these results we prove if V s proper sub-module of a module W over a ring D, then V is small 2-prime sub-module if and only if [V:W (d)] = V is a small 2-prime sub-module of W, for each d ∈ DD and d2∈[V:D W].</p>
      </abstract>
      <kwd-group>
        <kwd>Prime sub-module</kwd>
        <kwd>2-prime sub-module</kwd>
        <kwd>Small prime sub-module</kwd>
        <kwd>Small 2-prime sub-module</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>
