Localization in Non-Commutative Noetherian Rings
- 1 June 1976
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 28 (3) , 600-610
- https://doi.org/10.4153/cjm-1976-059-x
Abstract
To construct a well behaved localization of a noetherian ringRat a semiprime ideal S, it seems necessary to assume that the set(S)of moduloSregular elements satisfies the Ore condition ; and it is convenient to require the Artin Rees property for the Jacobson radical of the quotient ringRsin addition: one calls such 5classical.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.Keywords
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