First Order Calculi with Values in Right--Universal Bimodules

The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by--product we obtained intrinsic, coordinate--free and basis--independent generalization of the first order noncommutative differential calculi with partial derivatives.