Additive Biderivations of Incidence Algebras

Zhipeng Guan and Chi Zhang ()
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Zhipeng Guan: College of Sciences, Northeastern University, Shenyang 110004, China
Chi Zhang: College of Sciences, Northeastern University, Shenyang 110004, China

Mathematics, 2025, vol. 13, issue 19, 1-18

Abstract: 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.

Keywords: additive biderivation; incidence algebra; local finite poset; maximal chain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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