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  <doi_batch_id>aspg-33-1656-1792226232</doi_batch_id>
  <timestamp>20261017083712</timestamp>
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  <journal>
   <journal_metadata language="en">
    <full_title>Galoitica: Journal of Mathematical Structures and Applications</full_title>
    <abbrev_title>GJMSA</abbrev_title>
    <issn media_type="electronic">2834-5568</issn>
   </journal_metadata>
   <journal_issue>
    <publication_date media_type="online">
     <year>2023</year>
    </publication_date>
    <journal_volume>
     <volume>4</volume>
    </journal_volume>
    <issue>2</issue>
   </journal_issue>
   <journal_article publication_type="full_text">
    <titles>
     <title>A Representation of the Generators of the Quotients Group of Sl_2 By Matrices with Special Properties</title>
    </titles>
    <contributors>
     <person_name sequence="first" contributor_role="author">
      <given_name>Nader</given_name>
      <surname>Taffach</surname>
      <affiliations>
       <institution>
        <institution_name>Faculty of Science, Department of Mathematics, Idlib University, Syria.</institution_name>
       </institution>
      </affiliations>
     </person_name>
    </contributors>
    <jats:abstract>
     <jats:p>The problem of the existence and construction of a resolution of singularities is one of the central questions of algebraic geometry. In this paper, we study this problem in connecting with the quotients for</jats:p>
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     <jats:p>EN-US;mso-bidi-language:AR-SY'&gt;2 . It is known that the action of</jats:p>
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     <jats:p>EN-US;mso-bidi-language:AR-SY'&gt;2 on its Lie algebra is corresponding to the action of</jats:p>
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     <jats:p>dir=LTR&gt;3 . As a result of this action, it will be an invariant ring, which determines the quotients for</jats:p>
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     <jats:p>EN-US;mso-bidi-language:AR-SY'&gt;2 . This paper is devoted to studying the singularity of these quotients. We write this singularity as a matrix with interesting features such as, for example, its quadratic is a zero matrix and its rank is less than or equal to 1. Therefore, in this paper, we reduce the studying of the singularity of the quotients of</jats:p>
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     <jats:p>EN-US;mso-bidi-language:AR-SY'&gt;2 , which is a hard problem, to the studying of a matrix of invariants which is an easy problem.</jats:p>
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    <publication_date media_type="online">
     <year>2023</year>
    </publication_date>
    <pages>
     <first_page>24</first_page>
     <last_page>30</last_page>
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    <publisher_item>
     <item_number item_number_type="article-number">1656</item_number>
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     <doi>10.54216/GJMSA.040202</doi>
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