Reflexive ideals and completely faithful modules of Iwasawa algebras

Abstract

Let p≥5 be a prime number. Let G=H×Z, where H is a torsion free compact p-adic analytic group such that its Lie algebra is split semisimple over Qp and Z≅Znp, where n∈N0. We classify all the prime c-ideals of the Iwasawa algebra ΛG. Then we show the following: Let M be a finitely generated torsion ΛG-module, such that it has no non-zero pseudo-null submodules. Let q(M) denote the image of M in the quotient category mod-ΛG/CΛG1 via the quotient functor q, where CΛG1 denotes the Serre-subcategory of pseudo-null ΛG-modules in mod-ΛG. Then q(M) is completely faithful if and only if M is ΛZ-torsion free.