About: Derivative algebra (abstract algebra)

In abstract algebra, a derivative algebra is an algebraic structure of the signature <A, ·, +, ', 0, 1, D> where <A, ·, +, ', 0, 1> 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.