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    <Journal>
      <PublisherName>ijesm</PublisherName>
      <JournalTitle>International Journal of Engineering, Science and</JournalTitle>
      <PISSN>I</PISSN>
      <EISSN>S</EISSN>
      <Volume-Issue>volume 15,issue 8</Volume-Issue>
      <PartNumber/>
      <IssueTopic>Multidisciplinary</IssueTopic>
      <IssueLanguage>English</IssueLanguage>
      <Season>August 2026</Season>
      <SpecialIssue>N</SpecialIssue>
      <SupplementaryIssue>N</SupplementaryIssue>
      <IssueOA>Y</IssueOA>
      <PubDate>
        <Year>-0001</Year>
        <Month>11</Month>
        <Day>30</Day>
      </PubDate>
      <ArticleType>Engineering, Science and Mathematics</ArticleType>
      <ArticleTitle>STUDY OF SOME POLYNOMIAL IDENTITIES BUYING COMMUTATIVITY FOR RINGS</ArticleTitle>
      <SubTitle/>
      <ArticleLanguage>English</ArticleLanguage>
      <ArticleOA>Y</ArticleOA>
      <FirstPage>29</FirstPage>
      <LastPage>34</LastPage>
      <AuthorList>
        <Author>
          <FirstName>AMRIT KUMAR and Dr. Mukund Kumar</FirstName>
          <LastName>Singh</LastName>
          <AuthorLanguage>English</AuthorLanguage>
          <Affiliation/>
          <CorrespondingAuthor>N</CorrespondingAuthor>
          <ORCID/>
        </Author>
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      <DOI/>
      <Abstract>We know that a ring R is commutative if and only if [x, y] =0 for all x, y __ampersandsignisin; R.  It is natural to question whether a ring in which the commutators [xy, yx] are identically zero, be necessarily commutative. In 1970, Gupta [38] proved that a division ring is commutative if and only if [xy, yx] = 0. Earlier, Israel N. Herstein [45] established that a division ring D in which xy-yx is central for every pair of elements x,y __ampersandsignisin; D, must be commutative. Motivated by these results, Awtar [18] and Quadri [33] proved that a semi prime ring with either of [xy, yx] or xy o yx central, must also be commutative.</Abstract>
      <AbstractLanguage>English</AbstractLanguage>
      <Keywords/>
      <URLs>
        <Abstract>https://www.ijesm.co.in/ubijournal-v1copy/journals/abstract.php?article_id=16346&amp;title=STUDY OF SOME POLYNOMIAL IDENTITIES BUYING COMMUTATIVITY FOR RINGS</Abstract>
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      <References>
        <ReferencesarticleTitle>References</ReferencesarticleTitle>
        <ReferencesfirstPage>16</ReferencesfirstPage>
        <ReferenceslastPage>19</ReferenceslastPage>
        <References/>
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