1 Ocak 2015 Dergi makalesi Açık Erişim

Camillo, V.; Nicholson, W. K.

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/78537</identifier>
  <creators>
    <creator>
      <creatorName>Camillo, V.</creatorName>
      <givenName>V.</givenName>
      <familyName>Camillo</familyName>
      <affiliation>Univ Iowa, Dept Math, Iowa City, IA 52242 USA</affiliation>
    </creator>
    <creator>
      <creatorName>Nicholson, W. K.</creatorName>
      <givenName>W. K.</givenName>
      <familyName>Nicholson</familyName>
      <affiliation>Univ Calgary, Dept Math, Calgary, AB T2N 1N4, Canada</affiliation>
    </creator>
  </creators>
  <titles>
    <title>On Rings Where Left Principal Ideals Are Left Principal Annihilators</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2015</publicationYear>
  <dates>
    <date dateType="Issued">2015-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/78537</alternateIdentifier>
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  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.81043/aperta.78536</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.81043/aperta.78537</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>
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  <descriptions>
    <description descriptionType="Abstract">The rings in the title are studied and related to right principally injective rings. Many properties of these rings (called left pseudo-morphic by Yang) are derived, and conditions are given that an endomorphism ring is left pseudo-morphic. Some particular results: (1) Commutative pseudo-morphic rings are morphic; (2) Semiprime left pseudo-morphic rings are semisimple; and (3) A left and right pseudo-morphic ring satisfying (equivalent) mild finiteness conditions is a morphic, quasi-Frobenius ring in which every one-sided ideal is principal. Call a left ideal L a left principal annihilator if L = 1(a) = {r is an element of R vertical bar ra = 0} for some a is an element of R. It is shown that if R is left pseudo-morphic, left mininjective ring with the ACC on left principal annihilators then R is a quasi-Frobenius ring in which every right ideal is principal and every left ideal is a left principal annihilator.</description>
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