Abstract
In this paper we prove that under some natural conditions, the Ore extensions and skew Laurent polynomial rings are injectively homogeneous or homologically homogeneous if so are their coefficient rings. Specifically, we prove that ifR is a commutative Noetherian ring of positive characteristic, thenAn (R), thenth Weyl algebra overR, is injectively homogeneous (resp. homologically homogeneous) ifR has finite injective dimension (resp. global dimension).
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