Drmota, Michael; Skałba, Mariusz Relations between polynomial roots. (English) Zbl 0818.11038 Acta Arith. 71, No. 1, 65-77 (1995). This paper deals with multiplicative relations for roots of rational polynomials. In general it turns out that such relations are rare. In the case of abelian splitting fields a “classification” of those relations which may appear is provided. For example, there only exist irreducible polynomials with abelian Galois group such that one root is the product of two other roots if the degree is a multiple of 6. Reviewer: M.Skałba (Warszawa) Cited in 1 ReviewCited in 5 Documents MSC: 11R09 Polynomials (irreducibility, etc.) 11R20 Other abelian and metabelian extensions Keywords:polynomial roots; Tschirnhausen transformation; multiplicative relations; roots of rational polynomials; abelian splitting fields; abelian Galois group Citations:Zbl 0757.12001 PDFBibTeX XMLCite \textit{M. Drmota} and \textit{M. Skałba}, Acta Arith. 71, No. 1, 65--77 (1995; Zbl 0818.11038) Full Text: DOI EuDML