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Piecewise Noetherian Rings

Ponente: John Beachy
Institución: Department of Mathematical Sciences, Northern Illinois University.
Tipo de Evento: Investigación
Cuándo 25/05/2017
de 17:00 a 19:00
Dónde Salón Graciela Salicrup
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For a left Noetherian ring, Goldie defined the
notion of the reduced rank of a module, and it
has proved to be useful in studying Noetherian
rings. A more general torsion-theoretic
definition can be given, allowing us to consider
rings for which every factor ring has reduced rank
(and whose spectrum of prime ideals is Noetherian).
This condition is much weaker than Noetherian,
but does include rings with Krull dimension.
Small's example of a ring that is right but not
left Noetherian turns out to be piecewise Noetherian
on the left. This talk will explore some results
for such rings, and I plan to state a number of
open questions concerning them.