<?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-1635</article-id>
      <title-group>
        <article-title>Fuzzy visible submodules in the class of fuzzy faithful multiplication modules</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Mohammed</surname>
            <given-names>Sajda K.</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Education for Girls, University of Kufa, Kufa, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shihab</surname>
            <given-names>Buthyna N.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education Pure science (Ibn-Al-Haitham), University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>26</volume>
      <issue>6</issue>
      <fpage>1739</fpage>
      <lpage>1745</lpage>
      <pub-date date-type="pub">
        <day>01</day>
        <month>06</month>
        <year>2023</year>
      </pub-date>
      <abstract>
        <p>In this paper, the behavior of fuzzy visible submodules and its effect of it in the class of fuzzy faithful multiplication modules have been studied. Some relationship between fuzzy visible modules and fuzzy residual quotient ideals has been presented. Also, other properties with important results have been studied.</p>
      </abstract>
      <kwd-group>
        <kwd>Fuzzy visible modules</kwd>
        <kwd>Fuzzy residual ideals</kwd>
        <kwd>Fuzzy annihilator ideals</kwd>
        <kwd>Fuzzy multiplication submodules</kwd>
        <kwd>Fuzzy pure ideals</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>
