Yazar "Alagöz, Yusuf" seçeneğine göre listele

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    Öğe
    On M-injective and M-projective Modules
    (2020) Alagöz, Yusuf
    A left R-module M is called max-injective (or m-injective for short) if for any maximal left ideal I,any homomorphism f : I ? M can be extended to g : R ? M, if and only if Ext1R(R/I, M) = 0for any maximal left ideal I. A left R-module M is called max-projective (or m-projective for short)if Ext1R(M, N) = 0 for any max-injective left R-module N. We prove that every left R-module has aspecial m-projective precover and a special m-injective preenvelope. We characterize C-rings, SF ringsand max-hereditary rings using m-projective and m-injective modules.
  • [ X ]
    Öğe
    Weakly Poor Modules
    (Prof. Dr. Mehmet Zeki SARIKAYA, 2022) Alagöz, Yusuf
    In this paper, weakly poor modules are introduced as modules whose injectivity domains are contained in the class of all copure-split modules. This notion gives a generalization of both poor modules and copure-injectively poor modules. Properties involving weakly poor modules as well as examples that show the relations between weakly poor modules, poor modules, impecunious modules and copure-injectively poor modules are given. Rings over which every module is weakly poor are right CDS. A ring over which there is a cyclic projective weakly poor module is proved to be weakly poor. Moreover, the characterizations of weakly poor abelian groups is given. It states that an abelian group A is weakly poor if and only if A is impecunious if and only if for every prime integer p, A has a direct summand isomorphic to Zpn for some positive integer n. Consequently, an example of a weakly poor abelian group which is neither poor nor copure-injectively poor is given so that the generalization defined is proper. © 2022, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.