  Higher derivations on an associative algebra generalizes higher order
derivatives. We call a tuple consisting of an algebra and a higher derivation
on it by an AssHDer pair. We define a cohomology for AssHDer pairs with
coefficients in a representation. Next, we study central extensions, abelian
extensions of AssHDer pairs and relate them to the second cohomology group with
appropriate coefficients. Deformations of AssHDer pairs are also considered
which are governed by the cohomology with self coefficient.
