Abstract
Let [Formula: see text] be a derivation of a ring [Formula: see text], and let [Formula: see text] be the differential Ore extension of [Formula: see text] defined by putting [Formula: see text] for all [Formula: see text]. We describe the derivations of [Formula: see text] extending a derivation of [Formula: see text] and we deduce an explicit description of every derivation of [Formula: see text] in the case where [Formula: see text] is the polynomial ring [Formula: see text] over a field [Formula: see text]. As an application, we compute the first Hochschild cohomology group of [Formula: see text] when [Formula: see text] and [Formula: see text]; for [Formula: see text] a conjectural result is proposed.
Published Version
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