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REFLEXIVE IDEALS IN IWASAWA ALGEBRAS K. ARDAKOV, F. WEI AND J. J. ZHANG
 

Summary: REFLEXIVE IDEALS IN IWASAWA ALGEBRAS
K. ARDAKOV, F. WEI AND J. J. ZHANG
Abstract. Let G be a torsionfree compact p-adic analytic group. We give
suĂcient conditions on p and G which ensure that the Iwasawa
algebra
G of
G has no non-trivial two-sided re exive ideals. Consequently, these conditions
imply that every nonzero normal element
in
G is a unit. We show that these
conditions hold in the case when G is an open subgroup of SL 2 (Zp ) and p is
arbitrary. Using a previous result of the rst author, we show that there are
only two prime ideals
in
G when G is a congruence subgroup of SL 2 (Zp ): the
zero ideal and the unique maximal ideal. These statements partially answer
some questions asked by the rst author and Brown.
0. Introduction
0.1. Motivation. The Iwasawa theory for elliptic curves in arithmetic geometry
provides the main motivation for the study of Iwasawa algebras G , for example

  

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

 

Collections: Mathematics