Characterizing ring derivations of all orders via functional equations: results and open problems
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| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0256-8 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0256-8 | ||
| 100 | 1 | |a Ebanks |D Bruce |u Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, 39762, Mississippi State, MS, USA |4 aut | |
| 245 | 1 | 0 | |a Characterizing ring derivations of all orders via functional equations: results and open problems |h [Elektronische Daten] |c [Bruce Ebanks] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Ring derivation |2 nationallicence | |
| 690 | 7 | |a Derivation of higher order |2 nationallicence | |
| 690 | 7 | |a Additive map |2 nationallicence | |
| 690 | 7 | |a Homogeneous function |2 nationallicence | |
| 690 | 7 | |a Integral domain |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 685-718 |x 0001-9054 |q 89:3<685 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0256-8 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0256-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Ebanks |D Bruce |u Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, 39762, Mississippi State, MS, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 685-718 |x 0001-9054 |q 89:3<685 |1 2015 |2 89 |o 10 | ||