Let R be a noncommutative prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C. Let m,n ≥ 1 be fixed integers and F a nonzero generalized skew derivation of R. In this paper, we investigate the set S={F(xm)xn+xnF(xm):x ϵR} and prove that its left annihilator in R is identically zero. Using the above result, we also study the identity F(x)xn+xnF(x)=0 for semiprime rings.
On skew-commuting generalized skew derivations in prime and semiprime rings
Carini Luisa;De Filippis Vincenzo
2024-01-01
Abstract
Let R be a noncommutative prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C. Let m,n ≥ 1 be fixed integers and F a nonzero generalized skew derivation of R. In this paper, we investigate the set S={F(xm)xn+xnF(xm):x ϵR} and prove that its left annihilator in R is identically zero. Using the above result, we also study the identity F(x)xn+xnF(x)=0 for semiprime rings.File in questo prodotto:
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