Mathematics / Matematik

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

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End date: 2009Institution Author: search.filters.institutionAuthor.Alizade, Rafail

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 14
    Citation - Scopus: 14
    Cofinitely Weak Supplemented Lattices
    (Indian National Science Academy, 2009) Alizade, Rafail; Toksoy, Sultan Eylem
    In this paper it is shown that an E-complemented complete modular lattice L with small radical is weakly supplemented if and only if it is semilocal. L is a cofinitely weak supplemented lattice if and only if every maximal element of L has a weak supplement in L. If )α/0 is a cofinitely weak supplemented (weakly supplemented) sublattice and 1/α has no maximal element (1/α is weakly supplemented and a has a weak supplement in L), then L is cofinitely weak supplemented (weakly supplemented).
  • 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: 23
    Citation - Scopus: 23
    Cofinitely Weak Supplemented Modules
    (Taylor and Francis Ltd., 2003) Alizade, Rafail; Büyükaşık, Engin
    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.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Special Precovers in Cotorsion Theories
    (Cambridge University Press, 2002) Akıncı, Karen D.; Alizade, Rafail
    A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary cotorsion theories with an HC. Given a cotorsion theory with an HC, we consider the class of all modules having a special precover with respect to the first class in the cotorsion theory and show that this class is closed under extensions. We then raise the question of whether this class is resolving or coresolving.