Abstract
Let P be a partially ordered set (poset). The objective of the present paper is to introduce and study the idea of symmetric bi-derivations of posets. Several characterization theorems involving symmetric bi-derivations are given. In particular, we prove that if \(d_1\) and \(d_2\) are two symmetric bi-derivations of P with traces \(\phi _1\) and \(\phi _2,\) then \(\phi _1 \le \phi _2 \) if and only if \(\phi _{2}(\phi _{1}(x)) =\phi _1(x)\) for all \(x\in P\).
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Acknowledgements
The authors are deeply indebted to the learned referee(s) for their careful reading of the manuscript and constructive comments. The research of second named author is supported by SERB-DST MATRICS Project (Grant No. MTR/2019/000603), INDIA.
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Communicated by B. Sury.
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Abdelwanis, A.Y., Ali, S. Symmetric bi-derivations on posets. Indian J Pure Appl Math 54, 421–427 (2023). https://doi.org/10.1007/s13226-022-00263-4
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DOI: https://doi.org/10.1007/s13226-022-00263-4