On Dedekind domains whose class groups are direct sums of cyclic groups
Autor: | Chang, Gyu Whan, Geroldinger, Alfred |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | For a given family $(G_i)_{i \in \N}$ of finitely generated abelian groups, we construct a Dedekind domain $D$ having the following properties. \begin{enumerate} \item $\Pic(D) \cong \bigoplus_{i \in \N}G_i$. \item For each $i \in \N$, there exists a submonoid $S_i \subseteq D^{\bullet}$ with $\Pic (D_{S_i}) \cong G_i$. \item Each class of $\Pic (D)$ and of all $\Pic (D_{S_i})$ contains infinitely many prime ideals. \end{enumerate} Furthermore, we study orders as well as sets of lengths in the Dedekind domain $D$ and in all its localizations $D_{S_i}$. Comment: Journal of Pure and Applied Algebra, to appear |
Databáze: | arXiv |
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