Let R be a semiprime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R and {\$}{\$}n{\backslash}ge 1{\$}{\$}n≥1a fixed integer such that {\$}{\$}{\backslash}bigr (F(x)y+F(y)x-[x,y]{\backslash}bigl )^n=0{\$}{\$}(F(x)y+F(y)x-[x,y])n=0, for all {\$}{\$}x,y {\backslash}in R{\$}{\$}x,y∈R. Then R is commutative and {\$}{\$}F=0{\$}{\$}F=0.
A Commutativity Condition for Semiprime Rings with Generalized Skew Derivations
Rania F.
2024-01-01
Abstract
Let R be a semiprime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R and {\$}{\$}n{\backslash}ge 1{\$}{\$}n≥1a fixed integer such that {\$}{\$}{\backslash}bigr (F(x)y+F(y)x-[x,y]{\backslash}bigl )^n=0{\$}{\$}(F(x)y+F(y)x-[x,y])n=0, for all {\$}{\$}x,y {\backslash}in R{\$}{\$}x,y∈R. Then R is commutative and {\$}{\$}F=0{\$}{\$}F=0.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
