Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

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Access Right: Open AccessSubject: search.filters.subject.Injective modules

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  • 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.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    On the Structure of Modules Defined by Subinjectivity
    (World Scientific Publishing, 2019) Altınay, Ferhat; Büyükaşık, Engin; Durgun, Yılmaz
    The aim of this paper is to present new results and generalize some results about indigent modules. The commutative rings whose simple modules are indigent or injective are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. We show that a reduced module is indigent if and only if it is a Whitehead test module for injectivity over commutative hereditary noetherian rings. Furthermore, Dedekind domains are characterized by test modules for injectivity by subinjectivity.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 14
    Poor and Pi-Poor Abelian Groups
    (Taylor and Francis Ltd., 2017) Alizade, Rafail; Büyükaşık, Engin
    In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum of U(ℕ), where U ranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian group M, it is shown that M can not be torsion, and each p-primary component of M is unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Rad-supplements in injective modules
    (Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine, 2016) Büyükaşık, Engin; Tribak, Rachid
    We introduce and study the notion of Rad-sinjective modules (i.e. modules which are Rad-supplements in their injective hulls). We compare this notion with another generalization of injective modules. We show that the class of Rad-s-injective modules is closed under finite direct sums. We characterize Rads-injective modules over several type of rings, including semilocal rings, left hereditary rings and left Harada rings. © Journal “Algebra and Discrete Mathematics”.