JORDAN HIGHER DERIVATIONS, A NEW APPROACH | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 1، آذر 2022، صفحه 167-177 اصل مقاله (142.28 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10636.1527 | ||
| نویسنده | ||
| Sayed. Kh. Ekrami* | ||
| Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. | ||
| چکیده | ||
| Let $ \mathcal{A} $ be a unital algebra over a 2-torsion free commutative ring $ \mathcal{R} $ and $ \mathcal{M} $ be a unital $ \mathcal{A} $-bimodule. We show taht every Jordan higher derivation $ D=\{D_n\}_{n\in \mathbb{N}_0} $ from the trivial extension $ \mathcal{A} \ltimes \mathcal{M} $ into itself is a higher derivation, if $ PD_1(QXP)Q=QD_1(PXQ)P=0 $ for all $ X \in \mathcal{A} \ltimes \mathcal{M} $, in which $ P=(e,0) $ and $ Q=(e^\prime,0) $ for some non-trivial idempotent element $ e \in\mathcal{A} $ and $ e^\prime =1_\mathcal{A}-e $ satisfying the following conditions: $e\mathcal{A}e^\prime\mathcal{A}e=\{0\}$, $e^\prime\mathcal{A}e\mathcal{A}e^\prime=\{0\}$, $e(l.ann_\mathcal{A} \mathcal{M})e=\{0\}$, $e^\prime(r.ann_\mathcal{A} \mathcal{M})e^\prime=\{0\}$ and $ eme^\prime=m $ for all $ m \in \mathcal{M} $. | ||
| کلیدواژهها | ||
| Jordan higher derivation؛ Higher derivation؛ Trivial extension؛ Triangular algebra | ||
| مراجع | ||
|
[1] D. Benkovič, Jordan derivations and antiderivations on triangular matrices, Linear Algebra Appl., 397 (2005), 235–244. [2] E. Christensen, Derivations of nest algebras, Math. Ann., 229(2) (1977), 155– 161. [3] H. G. Dales, Banach Algebra and Automatic Continuity, Oxford: Oxford University Press. 2001. [4] K. R. Davidson, Nest Algebras, Pitman research notes in mathematics series 191, Longman Sci. Tech., Harlow, 1988. [5] H. R. Ebrahimi Vishki, M. Mirzavaziri and F. Moafian, Jordan higher derivations on trivial extension algebras, Commun. Korean Math. Soc., 31(2) (2016), 247–259. [6] A. Erfanian Attar, H. R. Ebrahimi Vishki, Jordan derivations on trivial extension algebras, J. Adv. Res. Pure Math., 6(4) (2014), 24–32. [7] M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaest. Math., 25 (2002), 249–257. [8] H. Ghahramani, Jordan Derivations on trivial extensions, Bull. Iranian Math. Soc., 39(4) (2013), 635–645. [9] H. Hasse and F. K. Schmidt, Noch eine Begrüdung der theorie der höheren Differential quotienten in einem algebraischen Funtionenkörper einer Unbestimmeten, J. Reine Angew. Math., 177 (1937), 215–237. [10] J. H. Zhang, W.Y. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl., 419 (2006), 251–255. | ||
|
آمار تعداد مشاهده مقاله: 803 تعداد دریافت فایل اصل مقاله: 724 |
||