Localization in Non-Commutative Noetherian Rings

Abstract

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.