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

A normal uniform algebra that fails to be strongly regular at a peak point