In the following year he published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory.
Sa mga sumusunod na taon siya nai-publish na Punong ideals at mahalaga-asa na may nakasulat na sama-sama ANG Cohen na malaki pinadali ang umiiral na proofs ng pagpunta-up at pagpunta-down theorems ng magandang theory.