Mathematics / Matematik

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

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End date: 2009Institution Author: search.filters.institutionAuthor.Büyükaşık, Engin

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 14
    Citation - Scopus: 11
    Extensions of Weakly Supplemented Modules
    (Mathematica Scandinavica, 2008) Alizade, Rafail; Büyükaşık, Engin; Büyükaşık, Engin; Alizade, Rafail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.
  • Article
    Citation - WoS: 26
    Citation - Scopus: 26
    On a Recent Generalization of Semiperfect Rings
    (Cambridge University Press, 2008) Büyükaşık, Engin; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In a recent paper by Wang and Ding, it was stated that any ring which is generalized supplemented as a left module over itself is semiperfect. The purpose of this note is to show that Wang and Ding's claim is not true and that the class of generalized supplemented rings lies properly between the classes of semilocal and semiperfect rings. Moreover, we propose a corrected version of the theorem by introducing a wider notion of 'local' for submodules. © 2008 Australian Mathematical Society.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    Cofinitely Weak Supplemented Modules
    (Taylor and Francis Ltd., 2003) Alizade, Rafail; Alizade, Rafail; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We prove that a module M is cofinitely weak supplemented or briefly cws (i.e., every submodule N of M with M/N finitely generated, has a weak supplement) if and only if every maximal submodule has a weak supplement. If M is a cws-module then every M-generated module is a cws-module. Every module is cws if and only if the ring is semilocal. We study also modules, whose finitely generated submodules have weak supplements.