Browsing by Author "Pancar, Ali"

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    On a new variation of injective modules
    (Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Türkmen, Ergül; Türkmen, Burcu Nişancı; Pancar, Ali; Nebiyev, Celil; Other; Other
    In this paper, we provide various properties of GE and GEE-modules, a new variation of injective modules. We call M a GE-module if it has a g-supplement in every extension N and, we call also M a GEE-module if it has ample g-supplements in every extension N. In particular, we prove that every semisimple module is a GE-module. We show that a module M is a GEE-module if and only if every submodule is a GE-module. We study the structure of GE and GEE-modules over Dedekind domains. Over Dedekind domains the class of GE-modules lies between WS-coinjective modules and Zöschinger's modules with the property (E). We also prove that, if a ring R is a local Dedekind domain, an R-module M is a GE-module if and only if M≅(R^{∗})ⁿ⊕K⊕N, where R^{∗} is the completion of R, K is injective and N is a bounded module.