This research reveals how additive biderivations can be uniquely split in posets over a commutative ring, suggesting new structural insights.
We characterize all additive biderivations on the incidence algebra I(P,R) of a locally finite poset P over a commutative ring with unity R. By decomposing P into its connected chains, we prove that any additive biderivation splits uniquely into a sum of inner biderivations and extremal ones determined by chain components. In particular, when every maximal chain of P is infinite, all additive biderivations are inner.
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Guan et al. (2025) studied this question.
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