<![CDATA[Various studies have explored the fascinating characteristics of modules over discrete valuation domain. One notable finding is that the multiplication module is regarded as indecomposable within a discrete valuation domain. Based on this distinctive property, a categorization of weak and pure multiplication modules over discrete valuation domain is established. A notable property of a discrete valuation ring is its role as the localization of a Dedekind domain. With this connection, there has been a classification of weak multiplication modules over the Dedekind domain. In this article, we examine the characteristics of the discrete valuation domain and the properties of pure multiplication modules over the discrete valuation domain, which collectively contribute to the properties of pure multiplication modules over the Dedekind domain. ]]>
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