If X is a noetherian subspace of Spec R, the set of primes of R[ x ] lying over X is also noetherian. A simple consequence is the theorem of Ohm and Pendleton that a ring module-finite over a ...

In this note we show that a Noetherian module has a dual module if and only if it satisfies $AB5^\ast$. A connection between completeness and $AB5^\ast$ is also ...