In
mathematics, a
derivation is a function on an
algebra which generalizes certain features of the
derivative operator. Specifically, given an algebra
A over a
ring or a
field K, a
K-derivation is a
K-
linear map that satisfies
Leibniz's law:
More generally, if
M is an
A-
bimodule, a
K-linear map that satisfies the Leibniz law is also called a derivation. The collection of all
K-derivations of
A to itself is denoted by Der
K(
A). The collection of
K-derivations of
A into an
A-module
M is denoted by .