Primeness, semiprimeness and localisation in Iwasawa algebras

Ardakov, Konstantin; Brown, Kenneth

doi:10.1090/S0002-9947-06-04153-5

Primeness, semiprimeness and localisation in Iwasawa algebras
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by Konstantin Ardakov and Kenneth A. Brown PDF

Trans. Amer. Math. Soc. 359 (2007), 1499-1515 Request permission

Abstract:

Necessary and sufficient conditions are given for the completed group algebras of a compact $p$-adic analytic group with coefficient ring the $p$-adic integers or the field of $p$ elements to be prime, semiprime and a domain. Necessary and sufficient conditions are found for the localisation at semiprime ideals related to the augmentation ideals of closed normal subgroups. Some information is obtained about the Krull and global dimensions of the localisations. The results extend and complete work of A. Neumann and J. Coates et al.

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