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Additive Biderivations of Incidence Algebras

Author

Listed:
  • Zhipeng Guan

    (College of Sciences, Northeastern University, Shenyang 110004, China)

  • Chi Zhang

    (College of Sciences, Northeastern University, Shenyang 110004, China)

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.

Suggested Citation

  • Zhipeng Guan & Chi Zhang, 2025. "Additive Biderivations of Incidence Algebras," Mathematics, MDPI, vol. 13(19), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3122-:d:1761284
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