Browsing by Author "Sipahi, Damla Dede"

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    Article
    Citation - WoS: 5
    Citation - Scopus: 8
    Modules and abelian groups with minimal (pure-) projectivity domains
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2017) Rafail Alizade; Damla Dede Sipahi; Alizade, Rafail; Sipahi, Damla Dede
    In this paper we give a complete description of the projectively poor abelian groups and prove that there exists a pure projectively poor abelian group. We show that over a commutative Artinian ring every module having a projectively poor factor module by a pure submodule is itself projectively poor. We also give some other properties of pure projectively poor modules.
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    Doctoral Thesis
    Saf projektif fakir modüller
    (2019) Sipahi, Damla Dede; Alizade, Refail
    In this thesis, (pure-) projective poor modules and p-impecunious modules are studied. Modules with pure projectivity domain equal to the class of pure split modules are called pureprojective poor modules (pp-poor); modules whose projectivity domain is equal to the class of semisimple modules are called projective poor modules (p-poor); modules whose projectivity domain is contained in the class of all pure split modules are called p-impecunious modules. It is shown that poor abelian groups and p-poor abelian groups coincide. Over Von Neumann regular ring, class of p-poor modules, pp-poor modules and p-impecunious modules are the same. The rings over which every right R-modules is p-impecunious are described. It is shown that abelian group A is p-impecunious if and only if Tp(A)≠0 for every prime number p. The rings over which every right R-modules is pp-poor rings are described. Let Mod-R be the class of all modules, I be the class of all injective modules, AP be the class of all absolutely pure modules and Ꭓ={X| Ext1(X;A) = 0 for every A ∈ AP}. It is shown that if there is a pp-poor module X from Ꭓ, then R is noetherian and all modules are in Ꭓ. It is proved that ⊕Ri, where {Ri}, i∈I is the set of all rational group is pp-poor group and there is no pp-poor group.