  Let $A$ be a nondegenerate dimer (or ghor) algebra on a torus, and let $Z$ be
its center. Using cyclic contractions, we show the following are equivalent:
$A$ is noetherian; $Z$ is noetherian; $A$ is a noncommutative crepant
resolution; each arrow of $A$ is contained in a perfect matching whose
complement supports a simple module; and the vertex corner rings $e_iAe_i$ are
pairwise isomorphic.
