<?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-2679</article-id>
      <title-group>
        <article-title>S-pseudo bounded modules</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Rashid</surname>
            <given-names>Amal Madhi</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shihab</surname>
            <given-names>Buthyna Najad</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>5</issue>
      <fpage>2077</fpage>
      <lpage>2082</lpage>
      <pub-date date-type="pub">
        <day>22</day>
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>The M is unitary module and F is commutative rings with identities. The definition of novel classes  F-modules that named, S-pseudo bounded modules for short (S-PS.B.). F- The modules has been studied. Our concept is based on the definition of S-pseudo bounded submodules, which was presented in a previous study. Furthermore, we highlight several known types of modules and clarify their relationships, including Dedekind, fully bounded, and quasi-injective modules, as well as other concepts. Finally, new results have been added on some types of modules related to S-PS.B. F-modules. </p>
      </abstract>
      <kwd-group>
        <kwd>Modules</kwd>
        <kwd>Dedekind module</kwd>
        <kwd>Rings</kwd>
        <kwd>Finitely generated module</kwd>
        <kwd>Quasi-injective 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>
