• Title/Summary/Keyword: $B{\acute{e}}zout$ modules

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GROUP GRADED TYPES OF BÉZOUT MODULES

  • Ahmed, Mamoon;Moh'D, Fida
    • Communications of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.523-534
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    • 2017
  • In this paper, we introduce two group graded types of $B{\acute{e}}zout$ modules, namely graded-$B{\acute{e}}zout$ modules and weakly graded-$B{\acute{e}}zout$ modules, which are two $B{\acute{e}}zout$ versions in Graded Module Theory. We investigate the relationship among the three types of $B{\acute{e}}zout$ modules, the ordinary $B{\acute{e}}zout$ modules and the two graded types of $B{\acute{e}}zout$ modules. Also, we study the structure of these new $B{\acute{e}}zout$ modules along with different properties; for instance, "A graded-$B{\acute{e}}zout$ R-module, with R being a Noetherian ring, is Noetherien iff it is gr-Noetherian".