<?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-2671</article-id>
      <title-group>
        <article-title>P-essential coessential submodules and P-essential coclosed submodules</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Mawlood</surname>
            <given-names>Ahmed K.</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>5</issue>
      <fpage>2019</fpage>
      <lpage>2025</lpage>
      <pub-date date-type="pub">
        <day>22</day>
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This work studies the concept for P-essential coessential submodules and P-essentials coclosed sub - module that is over commutating ring with identity. Consider Q as S-module with V ≤ W ≤ Q, then V is known a P-essential coessential submodule in Q of W if W/V  </p>
      </abstract>
      <kwd-group>
        <kwd>Small submodules</kwd>
        <kwd>Coessential submodules</kwd>
        <kwd>Coclosed submodules</kwd>
        <kwd>P-essential coessential submodules</kwd>
        <kwd>P-essential coclosed submodules</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>
