In mathematics:

• In abstract algebra and mathematical logic a derivative algebra is an algebraic structure that provides an abstraction of the derivative operator in topology and which provides algebraic semantics for the modal logic wK3.
• In abstract algebra, the derivative algebra of a not-necessarily associative algebra A over a field F is the subalgebra of the algebra of linear endomorphisms of A consisting of the derivations.
• In differential geometry a derivative algebra is a vector space with a product operation that has similar behaviour to the standard cross product of 3-vectors.^{[citation needed]}

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