DOI QR코드

DOI QR Code

ON JORDAN AND JORDAN HIGHER DERIVABLE MAPS OF RINGS

  • Liu, Lei (School of Mathematics and statistics Xidian University)
  • 투고 : 2019.07.05
  • 심사 : 2019.09.05
  • 발행 : 2020.07.31

초록

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.

키워드

과제정보

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

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