Let R be a prime ring of characteristic different from 2, {\$}{\$}Q{\_}r{\$}{\$}Qrits right Martindale quotient ring, F and G two non-zero generalized skew derivations of R, associated with the same automorphism {\$}{\$}{\backslash}alpha {\$}{\$}$\alpha$and commuting with {\$}{\$}{\backslash}alpha {\$}{\$}$\alpha$. In this work we describe all possible forms of F and G in the following two cases: (a) there exist {\$}{\$}a,b {\backslash}in Q{\_}r{\$}{\$}a,b∈Qrand a non-central Lie ideal L of R such that {\$}{\$}aF(x)b=0{\$}{\$}aF(x)b=0, for all {\$}{\$}x{\backslash}in L{\$}{\$}x∈L; (b) there exist {\$}{\$}a{\_}1,a{\_}2,b{\_}1,b{\_}2 {\backslash}in Q{\_}r{\$}{\$}a1,a2,b1,b2∈Qrsuch that {\$}{\$}a{\_}1F(x)b{\_}1+a{\_}2G(x)b{\_}2=0{\$}{\$}a1F(x)b1+a2G(x)b2=0, for all {\$}{\$}x{\backslash}in R{\$}{\$}x∈R.
Two Remarks on Generalized Skew Derivations in Prime Rings
Rania F.
2022-01-01
Abstract
Let R be a prime ring of characteristic different from 2, {\$}{\$}Q{\_}r{\$}{\$}Qrits right Martindale quotient ring, F and G two non-zero generalized skew derivations of R, associated with the same automorphism {\$}{\$}{\backslash}alpha {\$}{\$}$\alpha$and commuting with {\$}{\$}{\backslash}alpha {\$}{\$}$\alpha$. In this work we describe all possible forms of F and G in the following two cases: (a) there exist {\$}{\$}a,b {\backslash}in Q{\_}r{\$}{\$}a,b∈Qrand a non-central Lie ideal L of R such that {\$}{\$}aF(x)b=0{\$}{\$}aF(x)b=0, for all {\$}{\$}x{\backslash}in L{\$}{\$}x∈L; (b) there exist {\$}{\$}a{\_}1,a{\_}2,b{\_}1,b{\_}2 {\backslash}in Q{\_}r{\$}{\$}a1,a2,b1,b2∈Qrsuch that {\$}{\$}a{\_}1F(x)b{\_}1+a{\_}2G(x)b{\_}2=0{\$}{\$}a1F(x)b1+a2G(x)b2=0, for all {\$}{\$}x{\backslash}in R{\$}{\$}x∈R.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
