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.Buyukasik, EnginDepartment: search.filters.department.Izmir Institute of Technology

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  • Article
    On the Rings Whose Injective Right Modules Are Max-Projective
    (World Scientific Publ Co Pte Ltd, 2024) Alagoz, Yusuf; Büyükaşık, Engin; Buyukasik, Engin; Alagöz, Yusuf; Yurtsever, Haydar Baran; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of Science
    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
    A Note on Variants of Euler's Φ-Function
    (Univ debrecen, inst Mathematics, 2024) Buyukasik, Engin; Büyükaşık, Engin; Goral, Haydar; Göral, Haydar; Sertbas, Doga Can; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    It is well-known that the sum of the firstnconsecutive integers alwaysdivides thek-th power sum of the firstnconsecutive integers whenkis odd. Motivatedby this result, in this note, we study the divisibility properties of the power sum ofpositive integers that are coprime tonand not surpassingn. First, we prove a finitenessresult for our divisibility sets using smooth numbers in short intervals. Then, we findthe exact structure of a certain divisibility set that contains the orders of these powersums and our result is of computational flavour.