Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

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Access Right: Closed AccessAuthor: search.filters.author.Oyonarte, Luis

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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
    Rings Whose Mininjective Modules Are Injective
    (Taylor & Francis inc, 2025) Alagoz, Yusuf; Benli-Goral, Sinem; Buyukasik, Engin; Garcia Rozas, Juan Ramon; Oyonarte, Luis
    The main goal of this paper is to characterize rings over which the mininjective modules are injective, so that the classes of mininjective modules and injective modules coincide. We show that these rings are precisely those Noetherian rings for which every min-flat module is projective and we study this characterization in the cases when the ring is Kasch, commutative and when it is quasi-Frobenius. We also treat the case of nxn upper triangular matrix rings, proving that their mininjective modules are injective if and only if n=2. We use the developed machinery to find a new type of examples of indigent modules (those whose subinjectivity domain contains only the injective modules), whose existence is known, so far, only in some rather restricted situations.