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Free actions on semiprime rings

Muhammad Anwar Chaudhry, Mohammad S. Samman (2008)

Mathematica Bohemica

We identify some situations where mappings related to left centralizers, derivations and generalized ( α , β ) -derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation T , of a semiprime ring R the mapping ψ R R defined by ψ ( x ) = T ( x ) x - x T ( x ) for all x R is a free action. We also show that for a generalized ( α , β ) -derivation F of a semiprime ring R , with associated ( α , β ) -derivation d , a dependent element a of F is also a dependent element of α + d . Furthermore, we prove that for a centralizer f and...

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