Our aim is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings of algebraic curves at singular points. We characterize canonical ideals by means of a symmetry relation between lengths of certain quotients of associated ideals to a pair of dual ideals. In particular, we extend the symmetry among absolute and relative maximals in the sets of values of pairs of dual fractional ideals to other kinds of maximal points.
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