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Let $\mathcal{R}$ be a 2-torsion free unital ring containing a non-trivial idempotent. An additive map $\delta$ from $\mathcal{R}$ into itself is called a Jordan derivable map at commutative zero point if $\delta(AB+BA)=\delta(A)B+B\delta(A)+A\delta(B)+\delta(B)A$ for all $A, B\in\mathcal{R}$ with $AB=BA=0$. In this paper, we prove that, under some mild conditions, each Jordan derivable map at commutative zero point has the form $\delta(A)=\psi(A)+CA$ for all $A\in\mathcal{R}$, where $\psi$ is an additive Jordan derivation of $\mathcal{R}$ and $C$ is a central element of $\mathcal{R}$. Then we generalize the result to the case of Jordan higher derivable maps at commutative zero point. These results are also applied to some operator algebras.
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참고문헌 (16)
참고문헌 신청
Dominik Benkovič / 2005 / Jordan derivations and antiderivations on triangular matrices / Linear Algebra and its Applications 397:235~244
M. Bresar / 1988 / Jordan Derivations on Semiprime Rings / Proceedings of the American Mathematical Society 104(4):1003~1006
M. Bresar / 2007 / Characterizing homomorphisms, derivations and multipliers in rings with idem-potents / Proc. Roy. Soc. Edinburgh, Sect. A 137:9~21
Miguel Ferrero / 2002 / Higher Derivations and a Theorem By Herstein / Quaestiones Mathematicae 25(2):249~257
Miguel Ferrero / 2011 / HIGHER DERIVATIONS OF SEMIPRIME RINGS / Communications in Algebra 30(5):2321~2333
M. Bresar / 1988 / Jordan Derivations on Semiprime Rings / Proceedings of the American Mathematical Society 104(4):1003~1006
M. Bresar / 2007 / Characterizing homomorphisms, derivations and multipliers in rings with idem-potents / Proc. Roy. Soc. Edinburgh, Sect. A 137:9~21
Miguel Ferrero / 2002 / Higher Derivations and a Theorem By Herstein / Quaestiones Mathematicae 25(2):249~257
Miguel Ferrero / 2011 / HIGHER DERIVATIONS OF SEMIPRIME RINGS / Communications in Algebra 30(5):2321~2333
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