Abstract
We survey what is known about tame-wild dichotomy for commutative Noetherian rings. That is, we summarize terminology and results relating to the questions: “For which Noetherian rings does the category of finitely generated (or finite-length) modules have tame representation type?” and “For which rings do these categories have wild representation type?” We also address the question: “Can a Noetherian ring have both tame and wild representation type?” We provide an outline for showing that many tame rings are not wild.
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