The goal of this paper is to prove that the Pontryagin dual of the Selmer group over the trivializing extension of an elliptic curve without complex multiplication does not have any nonzero pseudo-null submodule. The main point is to extend the definition of pseudo-null to modules over the completed group ring Z p [[G]] of an arbitrary p-adic Lie group G without p-torsion. For this purpose we prove that Z p [[G]] is an Auslander regular ring. For the proof we also extend some results of

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... s homotopy theory of modules and study intensively higher Iwasawa adjoints.