TY - JOUR ID - 2329 TI - JORDAN HIGHER DERIVATIONS, A NEW APPROACH JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Ekrami, Sayed. Kh. AD - Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. Y1 - 2022 PY - 2022 VL - 10 IS - 1 SP - 167 EP - 177 KW - ‎Jordan higher derivation‎ KW - ‎Higher derivation‎ KW - ‎Trivial extension‎ KW - ‎Triangular algebra‎ DO - 10.22044/jas.2021.10636.1527 N2 - ‌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} $‌. UR - https://jas.shahroodut.ac.ir/article_2329.html L1 - https://jas.shahroodut.ac.ir/article_2329_9d17010f447376497c655730b9c58df1.pdf ER -