  It is shown that there exists a normal uniform algebra, on a compact
metrizable space, that fails to be strongly regular at some peak point. This
answers a 31-year-old question of Joel Feinstein. Our example is R(K) for a
certain compact planar set K. Furthermore, it has a totally ordered
one-parameter family of closed primary ideals whose hull is a peak point.
General results regarding lifting ideals under Cole root extensions are
established. These results are applied to obtain a normal uniform algebra, on a
compact metrizable space, with every point a peak point but again having a
totally ordered one-parameter family of closed primary ideals.
