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    Öğe
    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.
  • [ X ]
    Öğe
    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