Let A be a ({mathbb{k}})-algebra and ({A[t; lpha,delta]}) its Ore extension. We give a pair of adjoint functors between the module category over ker (delta) and the module category over ({A[t; lpha,delta]}). For a kind of special Ore extensions, this pair describes an equivalence between the module category over ker ({delta}) and an appropriate subcategory of the module category over ({A[t; lpha,delta]}). Applied to the case of Weyl algebras, this is exactly a Kashiwara’s theorem about D-modules.
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