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.Alagoz, YusufHas files: No

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  • Article
    Subinjectivity Relative To Cotorsion Pairs
    (MDPI, 2025) Alagoz, Yusuf; Alizade, Rafail; Buyukasik, Engin; Rozas, Juan Ramon Garcia; Oyonarte, Luis
    In this paper, we define and study the X-subinjectivity domain of a module M where X=(A,B) is a complete cotorsion pair, which consists of those modules N such that, for every extension K of N with K/N in A, any homomorphism f:N -> M can be extended to a homomorphism g:K -> M. This approach allows us to characterize some classical rings in terms of these domains and generalize some known results. In particular, we classify the rings with X-indigent modules-that is, the modules whose X-subinjectivity domains are as small as possible-for the cotorsion pair X=(FC,FI), where FI is the class of FP-injective modules. Additionally, we determine the rings for which all (simple) right modules are either X-indigent or FP-injective. We further investigate X-indigent Abelian groups in the category of torsion Abelian groups for the well-known example of the flat cotorsion pair X=(FL,EC), where FL is the class of flat modules.
  • Article
    On the Rings Whose Injective Right Modules Are Max-Projective
    (World Scientific Publ Co Pte Ltd, 2024) Alagoz, Yusuf; Buyukasik, Engin; Yurtsever, Haydar Baran
    Recently, right almost-QF (respectively, max-QF) rings that is the rings whose injective right modules are R-projective (respectively, max-projective) were studied by the first two authors. In this paper, our aim is to give some further characterizations of these rings over more general classes of rings, and address several questions about these rings. We obtain characterizations of max-QF rings over several classes of rings including local, semilocal right semihereditary, right non-singular right Noetherian and right non-singular right finite dimensional rings. We prove that for a ring R being right almost-QF and right max-QF are not left-right symmetric. We also show that right almost-QF and right max-QF rings are not closed under factor rings. This leads us to consider the rings all of whose factor rings are almost-QF and max-QF.