JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (12): 42-47.doi: 10.6040/j.issn.1671-9352.0.2017.255

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Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements

WU Li, ZHANG Jian-hua*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2017-05-22 Online:2017-12-20 Published:2017-12-22

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Abstract: Let U=Tri(A, M, B )be a 2-torsion free triangular algebra, and Q={u∈U:u2=0}. We prove that if a map φ:U→U satisfies φ(ab)=φ(a)b+aφ(b)for any a,b∈U with ［a,b］∈Q, then φ is an additive derivation, where ［a,b］=ab-ba is the Lie product and ab=ab+ba is the Jordan product.

Key words: square zero element, triangular algebra, Jordan derivable map

CLC Number: 

  • O177.1
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