Browsing by Author "Turkmen, Burcu Nisanci"

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    On rings with one middle class of injectivity domains
    (UNIV OSIJEK, DEPT MATHEMATICSUNIV OSIJEK, DEPT MATHEMATICS, TRG LJUDEVITA GAJA 6, OSIJEK HR-31000, CROATIA, 2022) Demirci, Yilmaz Mehmet; Alizade, Rafail; Turkmen, Burcu Nisanci; Turkmen, Ergul; 0000-0003-3802-4211; 0000-0003-4444-9136; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Demirci, Yilmaz Mehmet
    A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V-ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains.
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    Rings with modules having a restricted injectivity domain
    (SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND, 2019) Demirci, Yilmaz Mehmet; Turkmen, Burcu Nisanci; Turkmen, Ergul; 0000-0003-3802-4211; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü
    We introduce modules whose injectivity domains are contained in the class of modules with zero radical and call them working-class. This notion gives a generalization of poor modules that have minimal injectivity domain. Semisimple working-class modules always exist for arbitrary rings whereas their predecessors do not. We investigate the rings over which every module is either injective or working-class. Right weakly V-rings are examples of these rings. Moreover, we study the existence of working-class simple modules and show that if there is a projective working-class simple right module, then the ring is a right GV-ring.