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: 
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. 