Localisation at augmentation ideals in Iwasawa algebras
Let G be a compact p-adic analytic group and let AG be its completed group algebra with coefficient ring the p-adic integers ℤ p. We show that the augmentation ideal in Λ G of a closed normal subgroup H of G is localisable if and only if H is finite-...
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| स्वरूप: | Journal article |
| भाषा: | English |
| प्रकाशित: |
2006
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| सारांश: | Let G be a compact p-adic analytic group and let AG be its completed group algebra with coefficient ring the p-adic integers ℤ p. We show that the augmentation ideal in Λ G of a closed normal subgroup H of G is localisable if and only if H is finite-by-nilpotent, answering a question of Sujatha. The localisations are shown to be Auslander-regular rings with Krull and global dimensions equal to dim H. It is also shown that the minimal prime ideals and the prime radical of the double-struck F sign p-version Ω G of Λ G are controlled by Ω Δ+, where Δ + is the largest finite normal subgroup of G. Finally, we prove a conjecture of Ardakov and Brown [1]. © 2006 Glasgow Mathematical Journal Trust. |
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