turkmath.org

Injective hulls of simple modules over differential operator rings. Abstract: We consider Noetherian rings over which injective hulls of simple modules are locally Artinian. After a short motivation, we focus on the injective hulls of simple modules over differential operator rings, providing sufficient conditions under which these modules are not locally Artinian. As a consequence we characterize Ore extensions $S=K[x][y;\sigma, d]$ such that the injective hulls of simple $S$-modules are locally Artinian.