<?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-2280</article-id>
      <title-group>
        <article-title>Small subsemimodule and some related concepts</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Ali</surname>
            <given-names>Alaa Hussein</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, 51001, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Alhossaini</surname>
            <given-names>Asaad M. A.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, 51001, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>2</issue>
      <fpage>617</fpage>
      <lpage>623</lpage>
      <pub-date date-type="pub">
        <day>11</day>
        <month>04</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Previously, some authors have studied the concept of small submodules regarding semirings. This research aims to provide a comprehensive study of small modules and some related concepts as: cosemisimple semiring, semimodule with finite spanning dimension, small free semimodule and small projective semimodule. These concepts are implemented and studied in various modules. Then we convert it to semimodule and give some results.</p>
      </abstract>
      <kwd-group>
        <kwd>Subtractive semimodule</kwd>
        <kwd>Small subsemimodule</kwd>
        <kwd>Cosemisimple semiring</kwd>
        <kwd>Small projective semimodule</kwd>
        <kwd>Semimodule with finite spanning dimension</kwd>
        <kwd>Small free smimodule (S.F)</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>
