Mathematics / Matematik

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

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Has files: YesInstitution Author: search.filters.institutionAuthor.Durğun, Yılmaz

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  • 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.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 13
    Absolutely S-Pure Modules and Neat-Flat Modules
    (Taylor and Francis Ltd., 2015) Büyükaşık, Engin; Durğun, Yılmaz
    Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R-module is neat-flat. A commutative ring R is hereditary and noetherian if and only if every absolutely s-pure R-module is injective and R is nonsingular. If every simple right R-module is finitely presented, then (1)R R is absolutely s-pure if and only if R is right Kasch and (2) R is a right (Formula presented.) -CS ring if and only if every pure injective neat-flat right R-module is projective if and only if every absolutely s-pure left R-module is injective and R is right perfect. We also study enveloping and covering properties of absolutely s-pure and neat-flat modules. The rings over which every simple module has an injective cover are characterized. © 2015 Taylor & Francis Group, LLC.