Guo and the second author have shown that the closure in the Drury–Arveson space of a homogeneous principal ideal I in is essentially normal. In this note, the authors extend this result to the closure of any principal polynomial ideal in the Bergman space. In particular, the commutators and cross-commutators of the restrictions of the multiplication operators are shown to be in the Schatten p-class for . The same is true for modules generated by polynomials with vector-valued coefficients. Further, the maximal ideal space of the resulting -algebra for the quotient module is shown to be contained in , where is the zero variety for I, and to contain all points in that are limit points of . Finally, the techniques introduced enable one to study a certain class of weight Bergman spaces on the ball.