We prove that finitely generated n-SG-projective modules are infinitely presented.

This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, $\Lambda$ of a $p$-adic analytic group $G$. For $G$ without any $p$-torsion element we prove that $\Lambda$ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $\Lambda$-module. This is classical when $G={\mathbb{Z}}_p^k$ for some integer $k\ge 1$, but was previously unknown in the non-commutative case. Then the category of $\Lambda$-modules...