R.G. and Pérez proved that under certain conditions the test ideal of a module
closure agrees with the trace ideal of the module closure. We use this fact to compute
the test ideals of various rings with respect to the closures coming from their
indecomposable maximal Cohen–Macaulay modules. We also give an easier way to
compute the test ideal of a hypersurface ring in three variables coming from a module
with a particular type of matrix factorization.
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