Centres of skewfields and completely faithful Iwasawa modules

Abstract

Let H be a torsionfree compact p-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra \Lambda_H of H has trivial centre and use this result to classify the prime c-ideals in the Iwasawa algebra \Lambda_G of G := H \times \Zp. We also show that a finitely generated torsion \Lambda_G-module having no non-zero pseudo-null submodule is completely faithful if and only if it is has no central torsion. This has an application to the study of Selmer groups of elliptic curves.