<?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-1937</article-id>
      <title-group>
        <article-title>Neutrosophic invariant rings related with some applications</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Ali</surname>
            <given-names>Nibras H.</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Anbar, Ramadi, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Abed</surname>
            <given-names>Majid Mohammed</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Anbar, Ramadi, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>27</volume>
      <issue>5</issue>
      <fpage>1555</fpage>
      <lpage>1559</lpage>
      <pub-date date-type="pub">
        <day>26</day>
        <month>08</month>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>This article gives some new results of a notion namely neutrosophic invariant ring (NIR) and their relationship with an important module named multiplication module. Other properties have been presented in this paper. We proved (NC)-module over neutrosophic invariant ring is neutrosophic multiplication module. Also, neutrosophic f.generated is neutrosophic multiplication module over invariant ring. Finally, some remarks, examples and properties have introduced in this article.</p>
      </abstract>
      <kwd-group>
        <kwd>Invariant ring</kwd>
        <kwd>Neutrosophie ring</kwd>
        <kwd>Neutrosophic set</kwd>
        <kwd>Neutrosophic module</kwd>
        <kwd>Cyclic 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>
