Injective Hulls of Simple Modules over Differential Operator Rings

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

Key Words:

• Differential operator rings
• Injective modules
• Noetherian rings
• Simple modules

2010 Mathematics Subject Classification:

• 16P40
• 16S32
• 16D50

ACKNOWLEDGMENT

The authors would like to thank the referee for his/her careful reading and comments that improved the paper.

Notes

Communicated by J. Alev.