1 Ocak 2014 Dergi makalesi Açık Erişim

Keskin Tutuncu, Derya; Orhan Ertas, Nil; Smith, Patrick F.; Tribak, Rachid

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/65339</identifier>
  <creators>
    <creator>
      <creatorName>Keskin Tutuncu, Derya</creatorName>
      <givenName>Derya</givenName>
      <familyName>Keskin Tutuncu</familyName>
      <affiliation>Hacettepe Univ, Dept Math, Ankara, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Orhan Ertas, Nil</creatorName>
      <givenName>Nil</givenName>
      <familyName>Orhan Ertas</familyName>
      <affiliation>Karabuk Univ, Dept Math, Karabuk, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Smith, Patrick F.</creatorName>
      <givenName>Patrick F.</givenName>
      <familyName>Smith</familyName>
      <affiliation>Univ Glasgow, Dept Math, Glasgow, Lanark, Scotland</affiliation>
    </creator>
    <creator>
      <creatorName>Tribak, Rachid</creatorName>
      <givenName>Rachid</givenName>
      <familyName>Tribak</familyName>
      <affiliation>Reg Ctr Career Educ &amp; Training CRMEF Tangier, Tangier, Morocco</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Some Rings For Which The Cosingular Submodule Of Every Module Is A Direct Summand</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2014</publicationYear>
  <dates>
    <date dateType="Issued">2014-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/65339</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.3906/mat-1210-15</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">The snbmodule (Z)overbar(M) = boolean AND{N vertical bar M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if (Z)overbar(M) is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M is an element of Mod-R vertical bar &amp;lt;(Z)overbar &amp;gt;(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.</description>
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