Geodesic
On the Structure of Some Types of Higher Derivations
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 1, p. 123 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper we introduce the concepts of higher $\{L_{g_n}, R_{h_n}\}$-derivation, higher $\{g_n, h_n\}$-derivation and Jordan higher $\{g_n, h_n\}$-derivation. Then we give a characterization of higher $\{L_{g_n}, R_{h_n}\}$-derivations and higher $\{g_n, h_n\}$-derivations in terms of $\{L_g, R_h\}$-derivations and $\{g, h\}$-derivations, respectively. Using this result, we prove that every Jordan higher $\{g_n, h_n\}$-derivation on a semiprime algebra is a higher $\{g_n, h_n\}$-derivation. In addition, we show that every Jordan higher $\{g_n, h_n\}$-derivation of the tensor product of a semiprime algebra and a commutative algebra is a higher $\{g_n, h_n\}$-derivation. Moreover, we show that there is a one to one correspondence between the set of all higher $\{L_{g_n}, R_{h_n}\}$-derivations and the set of all sequences of $\{L_{G_n}, R_{H_n}\}$-derivations. Also, it is presented that if $\mathcal{A}$ is a unital algebra and $\{f_n\}$ is a generalized higher derivation associated with a sequence $\{d_n\}$ of linear mappings, then $\{d_n\}$ is a higher derivation. Some other related results are also discussed.
Classification : 16W25, 47B47
Keywords: higher $\{L_{g_n}, R_{h_n}\}$-derivation, higher $\{g_n, h_n\}$-derivation, Jordan higher $\{g_n, h_n\}$-derivation, generalized higher derivation 
@article{KJM_2024_48_1_a8,
     author = {Amin Hosseini and Nadeem Ur Rehman},
     title = {On the {Structure} of {Some} {Types} of {Higher} {Derivations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {123 },
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2024_48_1_a8/}
}
TY  - JOUR
AU  - Amin Hosseini
AU  - Nadeem Ur Rehman
TI  - On the Structure of Some Types of Higher Derivations
JO  - Kragujevac Journal of Mathematics
PY  - 2024
SP  - 123 
VL  - 48
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2024_48_1_a8/
LA  - en
ID  - KJM_2024_48_1_a8
ER  - 
%0 Journal Article
%A Amin Hosseini
%A Nadeem Ur Rehman
%T On the Structure of Some Types of Higher Derivations
%J Kragujevac Journal of Mathematics
%D 2024
%P 123 
%V 48
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2024_48_1_a8/
%G en
%F KJM_2024_48_1_a8
Amin Hosseini; Nadeem Ur Rehman. On the Structure of Some Types of Higher Derivations. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 1, p. 123 . http://geodesic.mathdoc.fr/item/KJM_2024_48_1_a8/