Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
Let $R$ be a prime ring with center $Z(R)$. A map $G\colon R\to R$ is called a multiplicative (generalized) $(\alpha,\beta)$-derivation if $G(xy) = G(x)\alpha(y)+\beta(x)g(y)$ is fulfilled for all $x,y\in R$, where $g\colon R\to R$ is any map (not necessarily derivation) and $\alpha,\beta\colon R\to R$ are automorphisms. Suppose that $G$ and $H$ are two multiplicative (generalized) $(\alpha,\beta)$-derivations associated with the mappings $g$ and $h$, respectively, on $R$ and $\alpha,\beta$ are automorphisms of $R$. The main objective of the present paper is to investigate the following algebraic identities: (i) $G(xy) + \alpha(xy) = 0$, (ii) $G(xy) + \alpha(yx) = 0$, (iii) $G(xy) + G(x)G(y) = 0$, (iv) $G(xy) = \alpha(y) \circ H(x)$ and (v) $G(xy) = [\alpha(y),H(x)]$ for all $x,y$ in an appropriate subset of $R$.(original abstract)
Twórcy
autor
- Aligarh muslim University Department of Mathematics
autor
- Ibb University Department of Mathematics ,
autor
- King Abdulaziz University Department of Mathematics, Faculty of Science
Bibliografia
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- B. Dhara and S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequationes Math. 86 (2013), no. 1-2, 65-79.
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- W.S. Martindale, III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21 (1969), no. 3, 695-698.
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Typ dokumentu
Bibliografia
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