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On the order of a derivation. (English) Zbl 1383.39022

Summary: In this note we provide the solution to a problem posed by the first author in a previous paper [Aequationes Math. 89, No. 3, 685–718 (2015; Zbl 1358.39010)]. In particular, we prove a result relating the number of nonzero coefficients of a certain functional equation to the order of any derivation satisfying that equation.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B72 Systems of functional equations and inequalities
13N15 Derivations and commutative rings
16W25 Derivations, actions of Lie algebras

Citations:

Zbl 1358.39010
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References:

[1] Ebanks, B.: Characterizing ring derivations of all orders via functional equations: results and open problems. Aeq. Math. 1-34 (2014) doi:10.1007/s00010-014-0256-8 · Zbl 1358.39010
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