In 1928 he defined the Krull dimension of a commutative Noetherian ring and brought ring theory into in new setting in which he was able to show that the principal ideal theorem held.
Sa 1928 na tinukoy niya ang Krull laki ng isang commutative Noetherian singsing at nagdala singsing sa teorya sa bagong setting sa kung saan siya ay upang ipakita na ang punong-guro ideal teorama gaganapin.