It is well-known that if $\Lambda=Z_p[[X]]$ and $M$ a finitely generated $\Lambda$-module, then $M$ is pseudo-isomorphic to $$ \Lambda^{\oplus r}\oplus\bigoplus_{i=1}^s\Lambda/(F_i) $$ for some integer $r$ and some irreducible elements $F_i$ of $\Lambda$.

I have seen a generalization of this result to multi-variable Iwasawa algebras, that is replacing $\Lambda$ by $Z_p[[X_1,\ldots,X_n]]$ for finitely generated torsion modules. In particular the free part always disappears. The standard reference seems to be Chapter VII of Bourbaki.

My question is, do we have the same structure theorem if we consider finitely generated modules, that are not necessarily torsion? If so, could someone provide a reference?

Thanks.

It is well-known that if $\Lambda=Z_p[[X]]$ and $M$ a finitely generated $\Lambda$-module, then $M$ is pseudo-isomorphic to $$ \Lambda^{\oplus r}\oplus\bigoplus_{i=1}^s\Lambda/(F_i) $$ for some integer $r$ and some irreducible elements $F_i$ of $\Lambda$.

I have seen a generalization of this result to multi-variable Iwasawa algebras, that is replacing $\Lambda$ by $Z_p[[X_1,\ldots,X_n]]$ for finitely generated torsion modules. In particular the free part always disappears. The standard reference seems to be Chapter VII of Bourbaki.

My question is, do we have the same structure theorem if we consider finitely generated modules, that are not necessarily torsion? If so, could someone provide a reference?