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A note on characterization of higher derivations and their product | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 1 - شماره پیاپی 26، بهمن 2023، صفحه 403-415 اصل مقاله (509.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.21376.1432 | ||
| نویسنده | ||
| Sayed Khalil Ekrami* | ||
| Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran | ||
| چکیده | ||
| There exists a one to one correspondence between higher derivations $\{d_n\}_{n=0}^\infty$ on an algebra $\mathcal{A}$ and the family of sequences of derivations $\{\delta_n\}_{n=1}^\infty$ on $\mathcal{A}$. In this paper, we obtain a relation that calculates each derivation $ \delta_n (n \in \mathbb{N})$ directly as a linear combination of products of terms of the corresponding higher derivation $\{d_n\}_{n=0}^\infty$. Also, we find the general form of the family of inner derivations corresponding to an inner higher derivation. We show that for every two higher derivations on an algebra $\mathcal{A}$, the product of them, is a higher derivation on $\mathcal{A}$. Also, we prove that the product of two inner higher derivations, is an inner higher derivation. | ||
| کلیدواژه‌ها | ||
| derivation؛ higher derivation؛ inner higher derivation | ||
| مراجع | ||
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