Characterizing ring derivations of all orders via functional equations: results and open problems

DOI10.1007/S00010-014-0256-8zbMath1358.39010OpenAlexW2053430212MaRDI QIDQ2350271

Bruce R. Ebanks

Publication date: 19 June 2015

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-014-0256-8

zbMATH Keywords

functional equationsintegral domainadditive maphomogeneous functionring derivationderivation of higher order

Mathematics Subject Classification ID

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

Related Items (20)

On the order of a derivation ⋮ Polynomially linked additive functions. II ⋮ A (possibly new) structure without the canonical base property ⋮ Derivations and Leibniz differences on rings ⋮ Linked pairs of additive functions ⋮ Polynomial equations for additive functions. I: The inner parameter case ⋮ Monomial functions, normal polynomials and polynomial equations ⋮ Quadratic functions fulfilling an additional condition along the hyperbola \(xy = 1 \) ⋮ Certain functional identities on division rings ⋮ Quadratic functions satisfying an additional equation ⋮ Conditional equations for quadratic functions ⋮ On derivations with respect to finite sets of smooth functions ⋮ A result related to derivations on unital semiprime rings ⋮ Functional equations characterizing derivations: a synthesis ⋮ Polynomially linked additive functions ⋮ When the image of a derivation on a uniformly complete \(f\)-algebra is contained in the radical ⋮ Derivations and Leibniz differences on rings: II ⋮ Functional equations characterizing derivations and homomorphisms on fields ⋮ On functional equations characterizing derivations: methods and examples ⋮ Reduction formulas for higher order derivations and a hypergeometric identity

Cites Work

• Homogeneous tri-additive forms and derivations
• On the equation \(F(X)+M(X)G(X^{-1})=0\) on \(K^ n\)
• The equation \(F(x)+M(x)G(1/x)=0\) and homogeneous biadditive forms
• The general solution of a functional equation related to the mixed theory of information
• On measures of information and their characterizations
• Characterization of field homomorphisms and derivations by functional equations
• Some relations between additive functions. I
• On a Generalized Fundamental Equation of Information
• The Definition of a Quadratic Form
• On a system of functional equations
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