Abstract
The purpose of this note is to present new proofs of two classical theorems in ideal theory, both due to W. Krull: the intersection theorem (see Krull(1) for the original proof, and Northcott (2), Chapter III, where the theorem is stated in the form proved below), and the principal ideal theorem ((1), or (2), Chapter III, Theorem 6). Both proofs depend on a device introduced by the author in (3) in another connexion.
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