Nonlinear Jordan derivations of incidence algebras

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Abstract
Let (X,≤) be a locally finite preordered set, R a two-torsion-free commutative ring with unity and I(X,R) the incidence algebra of X over R. In this paper, all the nonlinear Jordan derivations of I(X,R) are determined. In particular, if all the connected components of X are nontrivial, we prove that every nonlinear Jordan derivation of I(X,R) is proper and can be presented as a sum of an inner derivation, a transitive induced derivation, and an additive induced derivation.
Funding Information
  • National Natural Science Foundation of China (11701468)
  • Natural Science Foundation of Chongqing Municipality (cstc2019jcyj-msxmX0435)

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