caa a22 4500 605508550 CHVBK 20210128100637.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-014-0256-8 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0256-8 Ebanks Bruce Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, 39762, Mississippi State, MS, USA aut Characterizing ring derivations of all orders via functional equations: results and open problems [Elektronische Daten] [Bruce Ebanks] We provide a unifying framework for the treatment of equations of the form $$\sum_{k=1}^n x^{p_k} f_k (x^{q_k}) = 0$$ ∑ 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 integral domain of characteristic zero into itself. When negative exponents appear, we restrict our attention to fields of characteristic zero. All of the results could be formulated for integral domains or fields of sufficiently large characteristic as well. Springer Basel, 2014 Ring derivation nationallicence Derivation of higher order nationallicence Additive map nationallicence Homogeneous function nationallicence Integral domain nationallicence Aequationes mathematicae Springer Basel 89/3(2015-06-01), 685-718 0001-9054 89:3<685 2015 89 10 https://doi.org/10.1007/s00010-014-0256-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0256-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ebanks Bruce Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, 39762, Mississippi State, MS, USA aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 685-718 0001-9054 89:3<685 2015 89 10