We define a ring of skew differential operators on a commutative ring $A$ using a commutator twisted via the powers of an automorphism $\phi$ of $A$, derive some of the basic properties of this construction, and work out some examples. We show that many of the standard properties of differential operators continue to hold with our definition but that a crucial difference occurs for automorphisms of infinite order: frequently the action of a skew differential operator is then determined by its action on the powers of a single element of $A$.
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