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

Noetherian operators are differential that encode primary components of a polynomial ideal. We develop framework, as well algorithms, for computing with local dual spaces, both symbolically and numerically. For ideal, such provide an alternative representation to one given by set generators. This description fits numerical algebraic geometry, taking step toward the goal decomposition.