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.