Geodesic
A note on the invertible ideal theorem
Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 27-30

Voir la notice de l'article provenant de la source Cambridge University Press

This note is devoted to giving a conceptually simple proof of the Invertible Ideal Theorem [1, Theorem 4·6], namely that a prime ideal of a right Noetherian ring R minimal over an invertible ideal has rank at most one. In the commutative case this result may be easily deduced from the Principal Ideal Theorem by localizing and observing that an invertible ideal of a local ring is principal. Our proof is partially analogous in that it utilizes the Rees ring (denned below) in order to reduce the theorem to the case of a prime ideal minimal over an ideal generated by a single central element, which can be easily dealt with by adapting the commutative argument in [8]. The reader is also referred to the papers of Jategaonkar on the subject [5, 6, 7], particularly the last where another proof of the theorem appears which yields some additional information. 
Gray, Andy J. A note on the invertible ideal theorem. Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 27-30. doi: 10.1017/S0017089500005371
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