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Irreducibility Results for Compositions of Polynomials with Integer Coefficients

✍ Scribed by Anca Iuliana Bonciocat; Alexandru Zaharescu

Publisher
Springer Vienna
Year
2006
Tongue
English
Weight
123 KB
Volume
149
Category
Article
ISSN
0026-9255

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Let F βŠ‚ K be fields of characteristic 0, and let K x denote the ring of polynomials with coefficients in K. ∈ F for some j β‰₯ 1. Suppose that p ∈ K x , q ∈ K x \F x p not constant. Our main result is that p β€’ q / ∈ F x and D F p β€’ q = D F q . With only the assumption that a n b m ∈ F, we prove the i