A graded module is a module that is decomposed into a direct sum of submodules, each associated with a specific degree, allowing for the organization of its elements based on their degree of homogeneity. This structure is particularly useful in algebraic settings as it enables the analysis of the module's properties via its graded components. Graded modules are essential when working with Hilbert series and Hilbert functions, as they facilitate the understanding of how these series and functions capture the dimensions of graded components.
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