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Primeness, semiprimeness and localisation in Iwasawa algebras


Authors: Konstantin Ardakov and Kenneth A. Brown
Journal: Trans. Amer. Math. Soc. 359 (2007), 1499-1515
MSC (2000): Primary 16P40, 16L30, 11R23, 20C07
DOI: https://doi.org/10.1090/S0002-9947-06-04153-5
Published electronically: November 3, 2006
MathSciNet review: 2272136
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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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Additional Information

Konstantin Ardakov
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom
Email: K.Ardakov@dpmms.cam.ac.uk

Kenneth A. Brown
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
Email: kab@maths.gla.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-06-04153-5
Keywords: Noncommutative Iwasawa theory, pro-$p$ group, completed group algebra, complete noetherian local ring, prime ring, semiprime ring, localisable ideal
Received by editor(s): January 5, 2005
Published electronically: November 3, 2006
Additional Notes: The first author thanks Christ’s College, Cambridge, for financial support.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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