Abstract
We discuss the following three questions concerning multiplicative filtrations on commutative rings: (1) Must every filtration with finite power type be an AP-filtration? (2) Is the intersection of two AP-filtrations always an AP-filtration?, and (3) Does the multiplicity limit for a module of finite type with respect to a O-dimensional filtration on a noetherian ring always exist? We give examples to show that all three questions have in general negative answers for noetherian rings. However, in case of Dedekind domains the questions all have affirmative answers.
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