Injective hulls of simple modules over differential operator rings

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 of $S=K[x][θ;σ, d]$ for $d$ a $K$-linear derivation and $σ$ a $K$-linear automorphism of $K[x]$ such that injective hulls of simple $S$-modules are locally Artinian.

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