Abstract. We study injective hulls of simple modules over differential operator rings R[θ; d], providing necessary conditions under which these modules are locally Artinian. As a consequence we characterize Ore extensions ofsuch that injective hulls of simple S-modules are locally Artinian.
Using cocycle twists for associative graded algebras, we characterize finite dimensional nilpotent Lie color algebras L graded by arbitrary abelian groups whose enveloping algebras U (L) have the property that the injective hulls of simple right U (L)-modules are locally Artinian. We also collect together results on gradings on Lie algebras arising from this characterization.
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