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Let $R$ be an associative ring and $\alpha, \beta: R\rightarrow R$ ring homomorphisms. An additive mapping $d:R\rightarrow R$ is called an $(\alpha, \beta)$-derivation of $R$ if $d(xy)=d(x)\alpha(y)+\beta(x)d(y)$ is fulfilled for any $x,y \in R$, and an additive mapping $D:R\rightarrow R$ is called a generalized $(\alpha, \beta)$-derivation of $R$ associated with an $(\alpha, \beta)$-derivation $d$ if $D(xy)=D(x)\alpha(y)+\beta(x)d(y)$ is fulfilled for all $x,y \in R$. In this note, we intend to generalize a theorem of Vukman \cite{V}, and a theorem of Daif and El-Sayiad \cite{DS}.
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참고문헌 (5)
참고문헌 신청
S. Ali / 2008 / Jordan α-centralizer in rings and some aplications / Bol. Soc. Paran. Mat 26(1-2):71~80
M. N. Daif / 2007 / An Identity related to generalized derivations / Int. J. Algebra 1(9-12):547~550
M. Hongan / 2011 / Lie ideals and Jordan Triple derivations in rings / Rend. Sem. Mat. Univ. Padova 125:147~156
C. Lanski / 2007 / Generalized derivations and n-th power maps in rings / Comm. Algebra 35(11):3660~3672
J. Vukman / 2011 / Some remarks on derivations in semiprime rings and standard operator algebras / Glas. Mat. Ser. III 46(1):43~48
M. N. Daif / 2007 / An Identity related to generalized derivations / Int. J. Algebra 1(9-12):547~550
M. Hongan / 2011 / Lie ideals and Jordan Triple derivations in rings / Rend. Sem. Mat. Univ. Padova 125:147~156
C. Lanski / 2007 / Generalized derivations and n-th power maps in rings / Comm. Algebra 35(11):3660~3672
J. Vukman / 2011 / Some remarks on derivations in semiprime rings and standard operator algebras / Glas. Mat. Ser. III 46(1):43~48
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