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Relations between polynomial roots. (English) Zbl 0818.11038

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.

MSC:

11R09 Polynomials (irreducibility, etc.)
11R20 Other abelian and metabelian extensions

Citations:

Zbl 0757.12001
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