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.Alizade, RafailPublisher: search.filters.publisher.Taylor and Francis Ltd.

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 13
    Citation - Scopus: 14
    Poor and Pi-Poor Abelian Groups
    (Taylor and Francis Ltd., 2017) Alizade, Rafail; Alizade, Rafail; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum of U(ℕ), where U ranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian group M, it is shown that M can not be torsion, and each p-primary component of M is unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    The Proper Class Generated by Weak Supplements
    (Taylor and Francis Ltd., 2014) Alizade, Rafail; Demirci, Yılmaz Mehmet; Pusat, Dilek; Pusat, Dilek; Alizade, Rafail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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: 23
    Citation - Scopus: 23
    Cofinitely Weak Supplemented Modules
    (Taylor and Francis Ltd., 2003) Alizade, Rafail; Alizade, Rafail; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We prove that a module M is cofinitely weak supplemented or briefly cws (i.e., every submodule N of M with M/N finitely generated, has a weak supplement) if and only if every maximal submodule has a weak supplement. If M is a cws-module then every M-generated module is a cws-module. Every module is cws if and only if the ring is semilocal. We study also modules, whose finitely generated submodules have weak supplements.