$2$-Local Derivations on Finitary Incidence Algebras
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7218Keywords:
Finitary incidence algebra, local derivation, functional identitiesAbstract
Let \( P \) be a partially ordered set and \( R \) a commutative ring with identity. This paper investigates the finitary incidence algebra \( FI(P, R) \) and demonstrates that every \( R \)-linear local derivation on \( FI(P, R) \) is a derivation. Furthermore, we establish that when \( R \) possesses characteristic zero, every \( 2 \)-local derivation on \( FI(P, R) \) is also a derivation. Our proof builds upon functional identities and integrates insights from generalized Witt algebras. By examining the idempotent structure of \( FI(P, R) \), we show that \( 2 \)-local derivations do not exhibit any proper non-linear behavior.
References
Published
Issue
Section
License
Copyright (c) 2026 Majed Zailaee, Mohd Arif Raza, Abdul Khan
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.