LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS
Glasgow mathematical journal, Tome 48 (2006) no. 2, pp. 251-267
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Let $G$ be a compact $p$-adic analytic group and let $\Lambda_G$ be its completed group algebra with coefficient ring the $p$-adic integers $\mathbb{Z}_p$. We show that the augmentation ideal in $\Lambda_G$ 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 $\mathbb{F}_p$-version $\Omega_G$ of $\Lambda_G$ are controlled by $\Omega_{\Delta^+}$, where $\Delta^+$ is the largest finite normal subgroup of $G$. Finally, we prove a conjecture of Ardakov and Brown [1].
ARDAKOV, KONSTANTIN. LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS. Glasgow mathematical journal, Tome 48 (2006) no. 2, pp. 251-267. doi: 10.1017/S0017089506003041
@article{10_1017_S0017089506003041,
author = {ARDAKOV, KONSTANTIN},
title = {LOCALISATION {AT} {AUGMENTATION} {IDEALS} {IN} {IWASAWA} {ALGEBRAS}},
journal = {Glasgow mathematical journal},
pages = {251--267},
year = {2006},
volume = {48},
number = {2},
doi = {10.1017/S0017089506003041},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003041/}
}
TY - JOUR AU - ARDAKOV, KONSTANTIN TI - LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS JO - Glasgow mathematical journal PY - 2006 SP - 251 EP - 267 VL - 48 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003041/ DO - 10.1017/S0017089506003041 ID - 10_1017_S0017089506003041 ER -
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