A note on characterization of higher derivations and their product
| Autor: | Sayed Khalil Ekrami |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Journal of Mahani Mathematical Research, Vol 13, Iss 1, Pp 403-415 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2251-7952 2645-4505 |
| DOI: | 10.22103/jmmr.2023.21376.1432 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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