  The aim of this work 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. Our results generalize
and complement previous ones by other authors.
