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

• Published in: Aequationes mathematicae Vol. 89; no. 3; pp. 685 - 718
• Main Author: Ebanks, Bruce
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 01.06.2015; Springer Nature B.V
• Subjects: Analysis; Combinatorics; Mathematical functions; Mathematical problems; Mathematics; Mathematics and Statistics; Primary 39B52; Secondary 13N15; Derivation of higher order; 16W25; Homogeneous function; Integral domain; Additive map; 39B72; Ring derivation

We provide a unifying framework for the treatment of equations of the form ∑ k = 1 n x p k f k ( x q k ) = 0 for additive maps f k and integers p k , q k (1 ≤  k ≤  n ). We show how to solve many equations of this type, and we present some open problems. In general our unknown functions map an integ...