On noncommutative piecewise Noetherian rings. Issue 6 (3rd June 2017) - Bailey, Abigail C.; Beachy, John A.
ABSTRACT: We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.