Derivation

In abstract algebra, a derivation on an associative algebra A over a field k is a linear map D:A→A that satisfies Leibniz' law:

D(ab) = (Da)b + a(Db).

Examples of derivations are partial derivatives, Lie derivatives, the Pincherle derivative, and the commutator with respect to an element of the algebra. All these examples are tightly related, with the concept of derivation as the major unifying theme.

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Derivation may also be used as a synonym for proof, particularly for formulae.