نوع مقاله : مقاله پژوهشی
نویسنده
گروه ریاضی، دانشگاه پیام نور، صندوق پستی 3697-1939; تهران، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسنده [English]
Let $ \mathcal{A} $ and $ \mathcal{B} $ be two algebras and $ \lambda, \varphi $ and $ \psi $ be linear mappings from $ \mathcal{A} $ into $ \mathcal{B} $. $ \lambda $ is said to be a pexider Lie $ (\varphi,\psi) $-derivation, if $ \lambda([a_1,a_2])=[\varphi(a_1),a_2] + [a_1,\psi(a_2)]$ for all $ a_1,a_2 \in \mathcal{A} $, in which $[a_1,a_2]=a_1a_2 -a_2a_1$ is the Lie product of the elements $a_1,a_2 \in \mathcal{A}$.In this paper, we introduce the concept of a pexider Lie $ \{\Phi_n,\Psi_n\} $-higher derivation as a sequence of linear mappings $ \{\Lambda_n\}_{n=0}^\infty $ from $\mathcal{A}$ into $\mathcal{B}$ satisfying the equation\begin{equation*}\Lambda_n([a_1,a_2])=\sum_{i+j=n}[\Phi_i(a_1),\Psi_j(a_2)],\end{equation*}for all $ a_1,a_2 \in \mathcal{A} $ and all non-negative integers $ n $.
Then we characterize it in terms of sequence of pexider Lie $ \{\varphi_n,\psi_n\} $-derivations $ \{\lambda_n\}_{n=1}^\infty $ from $\mathcal{A}$ into $\mathcal{B}$. Also, we show that there is a one-to-one correspondence between the set of all pexider Lie $ \{\Phi_n,\Psi_n\} $-higher derivations $ \{\Lambda_n\}_{n=0}^\infty $ and the set of all sequences $ \{\lambda_n\}_{n=1}^\infty $ of pexider Lie $ \{\varphi_n,\psi_n\} $-derivations.
کلیدواژهها [English]
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