  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.
