Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON JORDAN AND JORDAN HIGHER DERIVABLE MAPS OF RINGS

  • Liu, Lei (School of Mathematics and statistics Xidian University)
  • Received : 2019.07.05
  • Accepted : 2019.09.05
  • Published : 2020.07.31
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Abstract

Let 𝓡 be a 2-torsion free unital ring containing a non-trivial idempotent. An additive map 𝛿 from 𝓡 into itself is called a Jordan derivable map at commutative zero point if 𝛿(AB + BA) = 𝛿(A)B + B𝛿(A) + A𝛿(B) + 𝛿(B)A for all A, B ∈ 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 𝛿(A) = 𝜓(A) + CA for all A ∈ 𝓡, where 𝜓 is an additive Jordan derivation of 𝓡 and C is a central element of 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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Acknowledgement

This work is Supported by National Natural Science Foundation of China(No. 11671078).

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