Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Alizade, RafailSubject: search.filters.subject.Hereditary condition

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  • Conference Object
    Resolutions in Cotorsion Theories
    (American Institute of Physics, 2010) Akıncı, Karen; Alizade, Rafail
    We consider the λ- (μ-) and λ̄- (μ̄-) dimensions of modules taken under a cotorsion theory (F, C) satisfying the Hereditary Condition, and establish some inequalities between the dimensions of the modules of a short exact sequence, not necessarily Hom (F, -) exact. We investigate the question of whether the property of having a (special) F- or C-resolution of length n is resolving, closed under extensions or coresolving and establish some inequalities connecting the λ- (μ-) and λ̄- (μ̄-) dimensions of modules in a short exact sequence. © 2010 American Institute of Physics.
  • 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.