Derivative algebra (abstract algebra)

In abstract algebra, a derivative algebra is an algebraic structure of the signature
 * 

where


 * 

is a Boolean algebra and D is a unary operator, the derivative operator, satisfying the identities:
 * 1) 0D = 0
 * 2) xDD ≤ x + xD
 * 3) (x + y)D = xD + yD.

xD is called the derivative of x. Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic wK4 = K + (p∧□p → □□p) that Boolean algebras play for ordinary propositional logic.