Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Publisher: search.filters.publisher.Mathematica ScandinavicaSubject: search.filters.subject.R-modules

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  • Article
    Citation - WoS: 14
    Citation - Scopus: 11
    Extensions of Weakly Supplemented Modules
    (Mathematica Scandinavica, 2008) Alizade, Rafail; Büyükaşık, Engin
    It is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is weakly supplemented. For a commutative ring R, we prove that R is semilocal if and only if every direct product of simple R-modules is weakly supplemented.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 14
    Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions
    (Mathematica Scandinavica, 2009) Büyükaşık, Engin; Lomp, Christian
    In this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.