WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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Access Right: Open AccessAuthor: search.filters.author.Buyukasik, Engin

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  • Article
    Virtually Regular Modules
    (World Scientific Publ Co Pte Ltd, 2025) Buyukasik, Engin; Demir, Ozlem Irmak
    In this paper, we call a right module M (strongly) virtually regular if every (finitely generated) cyclic submodule of M is isomorphic to a direct summand of M. M is said to be completely virtually regular if every submodule of M is virtually regular. In this paper, characterizations and some closure properties of the aforementioned modules are given. Several structure results are obtained over commutative rings. In particular, the structures of finitely presented (strongly) virtually regular modules and completely virtually regular modules are fully determined over valuation domains. Namely, for a valuation domain R with the unique nonzero maximal ideal P, we show that finitely presented (strongly) virtually regular modules are free if and only if P is not principal; and that P = Rp is principal if and only if finitely presented virtually regular modules are of the form R-n circle plus (R/Rp)(n)(1) circle plus (R/Rp(2))(n)(2) circle plus center dot center dot center dot circle plus (R/Rp(k))(n)(k) for nonnegative integers n, k, n(1), n(2),...,n(k). Similarly, we prove that P = Rp is principal if and only if finitely presented strongly virtually regular modules are of the form R-n circle plus (R/Rp)(m), where m,n are nonnegative integers. We also obtain that, R admits a nonzero finitely presented completely virtually regular module M if and only if P = Rp is principal. Moreover, for a finitely presented R-module M, we prove that: (i) if R is not a DVR, then M is completely virtually regular if and only if M congruent to( R/Rp)(m); and (ii) if R is a DVR, then M is completely virtually regular if and only if M congruent to R-n circle plus ( R/Rp)(m). Finally, we obtain a characterization of finitely generated virtually regular modules over the ring of integers.
  • 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.