Symmetric bi-derivations on posets

Ahmed Y. Abdelwanis () and Shakir Ali ()
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Ahmed Y. Abdelwanis: Cairo University
Shakir Ali: Aligarh Muslim University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 421-427

Abstract: 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 $$d_1$$ d 1 and $$d_2$$ d 2 are two symmetric bi-derivations of P with traces $$\phi _1$$ ϕ 1 and $$\phi _2,$$ ϕ 2 , then $$\phi _1 \le \phi _2 $$ ϕ 1 ≤ ϕ 2 if and only if $$\phi _{2}(\phi _{1}(x)) =\phi _1(x)$$ ϕ 2 ( ϕ 1 ( x ) ) = ϕ 1 ( x ) for all $$x\in P$$ x ∈ P .

Keywords: Derivation; Fixed point; Partially ordered set (poset); Symmetric bi-derivation; 06E20; 13N15; 06Axx (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00263-4

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