Beck modules and alternative algebras

We set out the general theory of Beck modules'' in a variety of algebras and describe them as modules over suitable universal enveloping’’ unital associative algebras. We develop a theory of ``noncommutative partial differentiation’’ to pass from the equations of the variety to relations in a universal enveloping algebra. We pay particular attention to the case of alternative algebras, defined by a restricted associative law, and determine the Poincaré polynomial of the universal enveloping algebra in the homogeneous case.