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The group algebra of all algebraic numbers

Here, we will get halfway into constructing $M_{cyc}$. We will try to understand the topology of the prime ideal spectrum $\mathbf{Spec}(\mathbb{C}[\overline{\mathbb{Q}}^{\times}])$ of the complex group algebra of the multiplicative group $\overline{\mathbb{Q}}^{\times}$ of all non-zero algebraic numbers. Take an Abelian locally compact group $A$ (for example, an Abelian group equipped with the discrete topology), then its.

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