Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Durğun, YılmazSubject: search.filters.subject.Coatomic modules

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  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Strongly Noncosingular Modules
    (Iranian Mathematical Society, 2016) Alagöz, Yusuf; Durğun, Yılmaz
    An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3) absolutely coneat modules are strongly noncosingular if and only if R is a right max ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    The Proper Class Generated by Weak Supplements
    (Taylor and Francis Ltd., 2014) Alizade, Rafail; Demirci, Yılmaz Mehmet; Durğun, Yılmaz; Pusat, Dilek
    We show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules coincide. Moreover, we show that this class can be obtained as a natural extension of the class determined by small submodules. We also study injective, projective, coinjective and coprojective objects of this class. We prove that it is coinjectively generated and its global dimension is at most 1. Finally, we describe this class for Dedekind domains in terms of supplement submodules.