<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03551892</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-02T14:37:17+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to factorizations of norms of algebraic integers</title>
            <author role="aut">
              <persName>
                <forename type="first">Safia</forename>
                <surname>Boukheche</surname>
              </persName>
              <idno type="halauthorid">2417055-0</idno>
              <affiliation ref="#struct-581232"/>
              <affiliation ref="#struct-92874"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Kamil</forename>
                <surname>Merito</surname>
              </persName>
              <idno type="halauthorid">1762656-0</idno>
              <affiliation ref="#struct-581232"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Oscar</forename>
                <surname>Ordaz</surname>
              </persName>
              <idno type="halauthorid">335752-0</idno>
              <orgName ref="#struct-89498"/>
              <affiliation ref="#struct-89498"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Wolfgang</forename>
                <surname>Schmid</surname>
              </persName>
              <email type="md5">e3e54c521065a548c34a667b0911a618</email>
              <email type="domain">math.univ-paris13.fr</email>
              <idno type="idhal" notation="string">wolfgang-schmid</idno>
              <idno type="idhal" notation="numeric">3112</idno>
              <idno type="halauthorid" notation="string">17238-3112</idno>
              <affiliation ref="#struct-78"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Wolfgang</forename>
                <surname>Schmid</surname>
              </persName>
              <email type="md5">e3e54c521065a548c34a667b0911a618</email>
              <email type="domain">math.univ-paris13.fr</email>
            </editor>
            <funder ref="#projanr-55954"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2022-02-02 01:25:17</date>
              <date type="whenWritten">2021-12</date>
              <date type="whenModified">2026-04-15 03:12:21</date>
              <date type="whenReleased">2022-02-07 21:12:51</date>
              <date type="whenProduced">2022-04-13</date>
              <date type="whenEndEmbargoed">2022-02-02</date>
              <ref type="file" target="https://hal.science/hal-03551892v1/document">
                <date notBefore="2022-02-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03551892v1/file/BMOS_art1_subm.pdf" id="file-3551892-3109444">
                <date notBefore="2022-02-02"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="172212">
                <persName>
                  <forename>Wolfgang</forename>
                  <surname>Schmid</surname>
                </persName>
                <email type="md5">e3e54c521065a548c34a667b0911a618</email>
                <email type="domain">math.univ-paris13.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03551892</idno>
            <idno type="halUri">https://hal.science/hal-03551892</idno>
            <idno type="halBibtex">boukheche:hal-03551892</idno>
            <idno type="halRefHtml">&lt;i&gt;Communications in Algebra&lt;/i&gt;, 2022, 50 (10), pp.4195-4217. &lt;a target="_blank" href="https://dx.doi.org/10.1080/00927872.2022.2058009"&gt;&amp;#x27E8;10.1080/00927872.2022.2058009&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Communications in Algebra, 2022, 50 (10), pp.4195-4217. &amp;#x27E8;10.1080/00927872.2022.2058009&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3551892-3109444"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-PARIS13">Université Paris-Nord - Paris XIII </idno>
            <idno type="stamp" n="UNIV-PARIS8" corresp="UNIV-PARIS-LUMIERES">Université Paris VIII Vincennes-Saint Denis</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="LAGA" corresp="UNIV-PARIS13">Laboratoire d'Analyse, Géométrie et Applications</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="OCA">Observatoire de la Cote d'Azur</idno>
            <idno type="stamp" n="GALILE" corresp="UNIV-PARIS13">Institut Galilée Université Paris 13</idno>
            <idno type="stamp" n="UNIV-PARIS-LUMIERES"/>
            <idno type="stamp" n="IBHGC" corresp="UNIV-PARIS13">Institut de Biomécanique Humaine Georges Charpak</idno>
            <idno type="stamp" n="SORBONNE-PARIS-NORD">Université Sorbonne Paris Nord</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UNIV-PARIS8-OA" corresp="UNIV-PARIS8">HAL UNIV-PARIS8 - open access</idno>
            <idno type="stamp" n="ACT-R" corresp="UNIV-PARIS13">Act'R </idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to factorizations of norms of algebraic integers</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Safia</forename>
                    <surname>Boukheche</surname>
                  </persName>
                  <idno type="halauthorid">2417055-0</idno>
                  <affiliation ref="#struct-581232"/>
                  <affiliation ref="#struct-92874"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Kamil</forename>
                    <surname>Merito</surname>
                  </persName>
                  <idno type="halauthorid">1762656-0</idno>
                  <affiliation ref="#struct-581232"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Oscar</forename>
                    <surname>Ordaz</surname>
                  </persName>
                  <idno type="halauthorid">335752-0</idno>
                  <orgName ref="#struct-89498"/>
                  <affiliation ref="#struct-89498"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Wolfgang</forename>
                    <surname>Schmid</surname>
                  </persName>
                  <email type="md5">e3e54c521065a548c34a667b0911a618</email>
                  <email type="domain">math.univ-paris13.fr</email>
                  <idno type="idhal" notation="string">wolfgang-schmid</idno>
                  <idno type="idhal" notation="numeric">3112</idno>
                  <idno type="halauthorid" notation="string">17238-3112</idno>
                  <affiliation ref="#struct-78"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">11925</idno>
                <idno type="issn">0092-7872</idno>
                <idno type="eissn">1532-4125</idno>
                <title level="j">Communications in Algebra</title>
                <imprint>
                  <publisher>Taylor &amp; Francis</publisher>
                  <biblScope unit="volume">50</biblScope>
                  <biblScope unit="issue">10</biblScope>
                  <biblScope unit="pp">4195-4217</biblScope>
                  <date type="datePub">2022-04-13</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1080/00927872.2022.2058009</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">norm</term>
                <term xml:lang="en">algebraic integer</term>
                <term xml:lang="en">zero-sum problem</term>
                <term xml:lang="en">weighted subsum</term>
                <term xml:lang="en">finite abelian group</term>
              </keywords>
              <classCode scheme="classification">MSC 11B30</classCode>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>The investigation of the arithmetic of monoids of zero-sum sequences over finite abelian groups is a classical subject due to their crucial role in understanding the arithmetic of (transfer) Krull monoids. More recently, sequences that admit, for a given set of weights, a weighted zero-sum received increased attention. Yet, the focus was on zero-sum constants rather than the arithmetic of the monoids formed by these sequences. We begin a systematic study of the arithmetic of these monoids. We show that for a wide class of weights unions of sets of lengths are intervals and we obtain various results on the elasticity of these monoids. More detailed results are obtained for the special case of plus-minus weighted sequences. Moreover, we apply our results to obtain results on factorizations of norms of algebraic integers.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-581232" status="VALID">
          <idno type="IdRef">086041142</idno>
          <idno type="ISNI">0000000106421613</idno>
          <idno type="RNSR">199712596J</idno>
          <idno type="ROR">https://ror.org/018nzqy79</idno>
          <orgName>Laboratoire Analyse, Géométrie et Applications</orgName>
          <orgName type="acronym">LAGA</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Institut Galilée, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.univ-paris13.fr/laga/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7539" active="#struct-11141" type="direct"/>
            <relation name="UMR7539" active="#struct-441569" type="direct"/>
            <relation name="UMR7539" active="#struct-581146" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92874" status="VALID">
          <orgName>Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]</orgName>
          <orgName type="acronym">USTHB</orgName>
          <desc>
            <address>
              <addrLine>BP 32 EL Alia 16111 Bab Ezzouar,  Alger</addrLine>
              <country key="DZ"/>
            </address>
            <ref type="url">http://www.usthb.dz/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-89498" status="VALID">
          <idno type="ISNI">0000000121550982</idno>
          <idno type="ROR">https://ror.org/05kacnm89</idno>
          <idno type="Wikidata">Q936476</idno>
          <orgName>Universidad Central de Venezuela = Central University of Venezuela</orgName>
          <orgName type="acronym">UCV</orgName>
          <desc>
            <address>
              <addrLine>Ciudad Universitaria, Los Chaguaramos Caracas</addrLine>
              <country key="VE"/>
            </address>
            <ref type="url">http://www.ucv.ve/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-78" status="OLD">
          <idno type="IdRef">086041142</idno>
          <idno type="ISNI">0000000106421613</idno>
          <idno type="RNSR">199712596J</idno>
          <idno type="ROR">https://ror.org/018nzqy79</idno>
          <orgName>Laboratoire Analyse, Géométrie et Applications</orgName>
          <orgName type="acronym">LAGA</orgName>
          <date type="start">1997-01-01</date>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.univ-paris13.fr/laga/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7539" active="#struct-11141" type="direct"/>
            <relation name="UMR7539" active="#struct-15786" type="direct"/>
            <relation active="#struct-301340" type="direct"/>
            <relation name="UMR7539" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-11141" status="VALID">
          <idno type="IdRef">026403552</idno>
          <idno type="ISNI">0000000121083026</idno>
          <idno type="ROR">https://ror.org/04wez5e68</idno>
          <orgName>Université Paris 8</orgName>
          <orgName type="acronym">UP8</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue de la Liberté - 93526 Saint-Denis cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris8.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-581146" status="VALID">
          <idno type="IdRef">02640463X</idno>
          <idno type="ISNI">0000000121496883</idno>
          <idno type="ROR">https://ror.org/0199hds37</idno>
          <orgName>Université Sorbonne Paris Nord</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>99, avenue Jean-Baptiste Clément, 93430 Villetaneuse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-paris13.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-15786" status="VALID">
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris 13</orgName>
          <orgName type="acronym">UP13</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-paris13.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301340" status="VALID">
          <orgName>Institut Galilée</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-55954" status="VALID">
          <idno type="anr">ANR-21-CE39-0009</idno>
          <orgName>BARRACUDA</orgName>
          <desc>Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications</desc>
          <date type="start">2021</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>