A derivation is a sequence of steps, logical or computational, from one result to another. The word derivation comes from the word "derive."
"Derivation" can also refer to an additive map 
on a ring 
satisfying 
for all 
. For an algebra over a
field, an algebra derivation is additionally linear
over that field. The derivations into the algebra
itself form its derivation algebra (Schafer
1996, pp. 3-4).
In particular, let 
be a Banach algebra and 
be a Banach A-bimodule.
Any element of
 |
is called a bounded derivation of 
in 
;
the identity is required for all 
. Any element of
 |
is called an inner derivation.
