Geodesic
Localization in Non-Commutative Noetherian Rings
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 600-610

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

To construct a well behaved localization of a noetherian ring R at a semiprime ideal S, it seems necessary to assume that the set (S) of modulo S regular elements satisfies the Ore condition ; and it is convenient to require the Artin Rees property for the Jacobson radical of the quotient ring R s in addition: one calls such 5 classical. To determine the classical semiprime ideals is no easy matter; it happens frequently that a prime ideal fails to be classical itself, but is minimal over a suitable classical semiprime ideal. 
Müller, Bruno J. Localization in Non-Commutative Noetherian Rings. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 600-610. doi: 10.4153/CJM-1976-059-x
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