Yazar "Demirci, Yilmaz Mehmet" seçeneğine göre listele

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    CLOSURES OF PROPER CLASSES
    (Univ Miskolc Inst Math, 2017) Alizade, Rafail; Demirci, Yilmaz Mehmet
    For an integral domain R we consider the closures (M) over cap ((M) over cap (r), r epsilon R) of a submodule M of an R-module N consisting of elements n of N with t n epsilon M (r(m) n epsilon M) for some nonzero t epsilon R (m epsilon Z(+)) and its connections with usual closure (M) over bar of M in N. Using these closures we study the closures (P) over cap and (P) over cap (r) of a proper class P of short exact sequences and give a decomposition for the class of quasi-splitting short exact sequences of abelian groups into the direct sum of p-closures of the class Split of splitting short exact sequences and description of closures of some classes. In the general case of an arbitrary ring we generalize these closures of a proper class P by means of homomorphism classes F and G and prove that under some conditions this closure (P) over cap (G)(F) is a proper classes.
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    Closures Of Proper Classes -2
    (University of Miskolc, 2017) Alizade, Rafail; Demirci, Yilmaz Mehmet
    For an integral domain R we consider the closures (formula persent) of a submodule M of an R-module N consisting of elements n of N with tn (formula persent) for some nonzero (formula persent) and its connections with usual closure M of M in N. Using these closures we study the closures (formula persent) of a proper class ℙ of short exact sequences and give a decomposition for the class of quasi-splitting short exact sequences of abelian groups into the direct sum of “p-closures” of the class Spl i t of splitting short exact sequences and description of closures of some classes. In the general case of an arbitrary ring we generalize these closures of a proper class ℙ by means of homomorphism classes ℱ and G and prove that under some conditions this closure (formula persent) is a proper classes. © 2017 Miskolc University Press
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    FLAT STRONG δ-COVERS OF MODULES
    (Ankara Univ, Fac Sci, 2019) Demirci, Yilmaz Mehmet
    We say that a ring R is right generalized delta-semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with delta-small kernel. This definition gives a generalization of both right delta-semiperfect rings and right generalized semiperfect rings. We provide examples involving such rings along with some of their properties. We introduce flat strong delta-cover of a module as a flat cover which is also a flat delta-cover and use flat strong delta-covers in characterizing right A-perfect rings, right B-perfect rings and right perfect rings.
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    Modules and abelian groups with a bounded domain of injectivity
    (World Scientific Publ Co Pte Ltd, 2018) Demirci, Yilmaz Mehmet
    In this work, impecunious modules are introduced as modules whose injectivity domains are contained in the class of all pure-split modules. This notion gives a generalization of both poor modules and pure-injectively poor modules. Properties involving impecunious modules as well as examples that show the relations between impecunious modules, poor modules and pure-injectively poor modules are given. Rings over which every module is impecunious are right pure-semisimple. A commutative ring over which there is a projective semisimple impecunious module is proved to be semisimple artinian. Moreover, the characterization of impecunious abelian groups is given. It states that an abelian group M is impecunious if and only if for every prime integer p, M has a direct summand isomorphic to Z(p)(n) for some positive integer n. Consequently, an example of an impecunious abelian group which is neither poor nor pure-injectively poor is given so that the generalization defined is proper.