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If is a hereditary torsion theory on and is the localization functor, then we show that every -derivation has a unique extension to an -derivation when is a differential torsion theory on . Dually, it is shown that if is cohereditary and is the colocalization functor, then every -derivation can be lifted uniquely to an -derivation .
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 obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.
We identify some situations where mappings related to left centralizers, derivations and generalized -derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation , of a semiprime ring the mapping defined by for all is a free action. We also show that for a generalized -derivation of a semiprime ring with associated -derivation a dependent element of is also a dependent element of Furthermore, we prove that for a centralizer and...
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