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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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:
  • Kenneth A. Brown
  • Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
  • MR Author ID: 42135
  • ORCID: 0000-0003-3497-3372
  • Email:
  • Received by editor(s): January 5, 2005
  • Published electronically: November 3, 2006
  • Additional Notes: The first author thanks Christโ€™s College, Cambridge, for financial support.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 1499-1515
  • MSC (2000): Primary 16P40, 16L30, 11R23, 20C07
  • DOI:
  • MathSciNet review: 2272136