Skew derivations on partially ordered sets

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, 2021, vol. 52, issue 4, 1256-1262

Abstract: Abstract Let P be a poset and $$\alpha :P\rightarrow P$$ α : P → P be a function. The aim of this paper is to introduce and study the notion of skew derivations on P. We prove some fundamental properties of posets involving skew derivations. In particular, apart from proving the other results, we prove that if d and g are two skew derivations of P associated with an automorphism $$\alpha $$ α such that $$d\alpha =\alpha d$$ d α = α d and $$g\alpha =\alpha g,$$ g α = α g , then $$d \le g $$ d ≤ g if and only if $$g d =\alpha d$$ g d = α d . Also, we prove that $$ Fix_{\alpha ,d}(P)\cap l(\alpha (x)) = l(d(x))$$ F i x α , d ( P ) ∩ l ( α ( x ) ) = l ( d ( x ) ) for all $$x\in P.$$ x ∈ P . Furthermore, we give some examples to demonstrate that various restrictions imposed in the hypotheses of our results are not superfluous.

Keywords: Derivation; $$\alpha $$ α -fixed point; Ideal; Poset; Skew derivation; 06E20; 13N15; 06Axx (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00036-5

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