Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Projectivity and Quasi-Projectivity With Respect To Epimorphisms To Simple Modules(World Scientific Publ Co Pte Ltd, 2025) Alagoz, Yusuf; Alizade, Rafail; Buyukasik, EnginUsing the notion of relative max-projectivity, max-projectivity domain of a module is investigated. Such a domain includes the class of all modules whose maximal submodules are direct summands (this class denoted as MDMod -R). We call a module max-p-poor if its max-projectivity domain is exactly the class MDMod -R. We establish the existence of max-p-poor modules over any ring. Furthermore, we study commutative rings whose simple modules are projective or max-p-poor. Additionally, we determine the right Noetherian rings for which all right modules are projective or p-poor. Max-p-poor abelian groups are fully characterized and shown to coincide precisely with p-poor abelian groups. We also further investigate modules that are max-projective relative to themselves, which are known as simple-quasi-projective modules. Several properties of these modules are provided, and the structure of certain classes of simple-quasi-projective modules is determined over specific commutative rings including the ring of integers and valuation domains.Article Subinjectivity Relative To Cotorsion Pairs(MDPI, 2025) Alagoz, Yusuf; Alizade, Rafail; Buyukasik, Engin; Rozas, Juan Ramon Garcia; Oyonarte, LuisIn 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, LuisThe 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.Article On the Rings Whose Injective Right Modules Are Max-Projective(World Scientific Publ Co Pte Ltd, 2024) Alagoz, Yusuf; Buyukasik, Engin; Yurtsever, Haydar BaranRecently, 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.