Author:
Liang Xinfeng,Zhao Lingling
Abstract
<abstract><p>The purpose of this article is to prove that every bi-Lie n-derivation of certain triangular rings is the sum of an inner biderivation, an extremal biderivation and an additive central mapping vanishing at $ (n-1)^{th} $-commutators for both components, using the notion of maximal left ring of quotients. As a consequence, we characterize the decomposition structure of bi-Lie n-derivations on upper triangular matrix rings.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference17 articles.
1. G. Maksa, On the trace of symmetric biderivations, C. R. Math. Rep. Acad. Sci. Canada., 9 (1987), 303–308.
2. G. Maksa, A remark on symmetric biadditive functions having nonnegative diagonalization, Glasnik Math., 15 (1980), 279–282.
3. Y. Wang, Biderivations of triangular rings, Linear Multilinear Algebra, 64 (2016), 1952–1959. https://doi.org/10.1080/03081087.2015.1127887
4. N. M. Ghosseiri, On biderivations of upper triangular matrix rings, Linear Algebra Appl., 438 (2013), 250–260. https://doi.org/10.1016/j.laa.2012.07.039
5. Y. Wang, On functional identities of degree 2 and centralizing maps in triangular rings, Oper. Matrices, 10 (2016), 485–499. https://doi.org/10.7153/oam-10-28