On normal precipitous ideals

An old question of T. Jech and K Prikry asks whether the existence of a precipitous ideal implies the existence of a normal precipitous one. The aim of the paper is to prove some results in the positive direction. In particular, it is shown that under some mild assumptions, the existence of a precipitous ideal over א₁ implies the existence of a normal precipitous ideal over א₁ once a Cohen subset is added to א₂.