Mathematics / Matematik

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

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Subject: search.filters.subject.R-modulesWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Strongly Noncosingular Modules
    (Iranian Mathematical Society, 2016) Alagöz, Yusuf; Durğun, Yılmaz
    An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3) absolutely coneat modules are strongly noncosingular if and only if R is a right max ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.
  • 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.