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 a particular type of operator used to define a derivation algebra on a ring or algebra. In particular, let A be a Banach algebra and X be a Banach A-bimodule. Any element of

 Z^1(A,X)={delta:A->X;delta is bounded, linear and  

is called a bounded derivation of A in X and any element of

 a in A,x in X}

is called an inner derivation.

See also

Derivation Algebra

Portions of this entry contributed by Todd Rowland

Portions of this entry contributed by Mohammad Sal Moslehian

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Helemskii, A. Ya. The Homology of Banach and Topological Algebras. Dordrecht, Netherlands: Kluwer, 1989.Helemskii, A. Ya. Banach and Locally Convex Algebras. Oxford, England: Oxford University Press, 1993.Helemskii, A. Ya. "The Homology in Algebra of Analysis." In Handbook of Algebra, Vol. 2. Amsterdam, Netherlands: Elsevier, 1997.

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Cite this as:

Moslehian, Mohammad Sal; Rowland, Todd; and Weisstein, Eric W. "Derivation." From MathWorld--A Wolfram Web Resource.

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