Free actions on prime and semiprime rings

Abstract EN

Let R be an associative ring with center Z(R).

We identify some situations where mappings related to left reverse-centralizer, derivations are free actions on prime and semiprime rings.

We show that for a left reverse - centralizer of a semiprime ring R the mapping ψ:R→ R defined by ψ (x)= [T (x), X], for all x € R is a free action.

We also show that for a generalized derivation F of a semi prime ring R , if a € R is a dependent element of F, then a € Z (R).

furthermore, we prove that for a left reverse-centralizer T and a derivation d of a prime ring R, ψ = T º d isa free action.