1 Ocak 2014 Dergi makalesi Açık Erişim

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

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{
  "@context": "https://schema.org/", 
  "@id": 65339, 
  "@type": "ScholarlyArticle", 
  "creator": [
    {
      "@type": "Person", 
      "affiliation": "Hacettepe Univ, Dept Math, Ankara, Turkey", 
      "name": "Keskin Tutuncu, Derya"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Karabuk Univ, Dept Math, Karabuk, Turkey", 
      "name": "Orhan Ertas, Nil"
    }, 
    {
      "@type": "Person", 
      "affiliation": "Univ Glasgow, Dept Math, Glasgow, Lanark, Scotland", 
      "name": "Smith, Patrick F."
    }, 
    {
      "@type": "Person", 
      "affiliation": "Reg Ctr Career Educ & Training CRMEF Tangier, Tangier, Morocco", 
      "name": "Tribak, Rachid"
    }
  ], 
  "datePublished": "2014-01-01", 
  "description": "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 <(Z)overbar >(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.", 
  "headline": "Some rings for which the cosingular submodule of every module is a direct summand", 
  "identifier": 65339, 
  "image": "https://aperta.ulakbim.gov.tr/static/img/logo/aperta_logo_with_icon.svg", 
  "license": "http://www.opendefinition.org/licenses/cc-by", 
  "name": "Some rings for which the cosingular submodule of every module is a direct summand", 
  "url": "https://aperta.ulakbim.gov.tr/record/65339"
}