Universal localization of piecewise Noetherian rings

Ponente(s): John Beachy .

Modeling the commutative case, the universal localization of a noncommutative ring R at a prime ideal P is the ring universal with respect to the property that modulo its Jacobson radical it is isomorphic to the classical ring of quotients of R/P. For Noetherian rings, the construction of the universal localization was given by P.M.Cohn in 1973, but the progress in understanding its applications has been slow. This talk will consider certain results that can be extended from Noetherian rings to the broader class of piecewise Noetherian rings. (A ring is called piecewise Noetherian if it has a Noetherian spectrum and for each prime ideal P the set of P-primary left ideals satisfies the ascending chain condition.)