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Keywords:
graded duplication; duplication of a module; graded amalgamated duplication; graded Noetherian; graded coherent
graded duplication; duplication of a module; graded amalgamated duplication; graded Noetherian; graded coherent
Summary:
We investigate the graded duplication of modules and amalgamated rings along homogeneous ideals in a commutative monoid-graded ring. Specifically, we introduce the concept of the graded duplication of an $R$-module $M$ along an ideal $I$, and we explore its fundamental properties. We provide characterizations of graded prime submodules and the transfer of Noetherian and Artinian properties to the graded duplication. Additionally, we extend our results to graded coherent and graded Nil$_{*}$ coherent modules, examining conditions under which these properties hold in the context of amalgamated duplication. Our results generalize several known results in the graded ring theory, providing new insights into the structure of graded modules.
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