Tuesday, June 25, 14:00, 7.527

Paula Carvalho (Porto), Injective modules over Noetherian rings.

Abstract:

In 1958 Matlis showed that any indecomposable injective module over a commutative Noetherian ring is isomophic to the injective hull of some prime factor of the ring. Also in the same paper it was proved that the injective hull of any simple module is Artinian. Motivated by applications to Jacobson's conjecture, Jategaonkar proved in 1974 that over fully bounded Noetherian rings the injective hull of simple modules are locally Artinian, thus incorporating Noetherian rings satisfying a polynomial identity and so generalising the commutative case.

A Noetherian ring whose simple modules have the property that their finitely generated essential extension are Artinian is said to satisfy property (⋄). In the first part of this talk I will present a brief survey of the work on this topic. The second part of the talk is dedicated to the case of skew polynomial rings based on joint work with Ken Brown and Jerzey Matczuk.