Reflexive ideals in Iwasawa algebras

• Autores: Konstantin Ardakov, F. Wei, James J. Zhang
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 3, 2008, págs. 865-901
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.02.004
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• Resumen

  • Let G be a torsionfree compact p-adic analytic group. We give sufficient conditions on p and G which ensure that the Iwasawa algebra OG of G has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every non-zero normal element in OG is a unit. We show that these conditions hold in the case when G is an open subgroup of and p is arbitrary. Using a previous result of the first author, we show that there are only two prime ideals in OG when G is a congruence subgroup of : the zero ideal and the unique maximal ideal. These statements partially answer some questions asked by the first author and Brown