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Polynomials with a common composite. (English) Zbl 1195.12002

The paper contains a wealth of results, both new and old (but with fresh proofs using only on elementary properties of polynomials) dealing with common composites of two polynomials over a field of arbitrary characteristic. One of the new results (Theorem 1.1) provides a necessary and sufficient condition for the existence of such a composite, and another (Theorem 5.1) shows that in zero characteristic only few pairs of polynomials can have a common composite. Two algorithms are provided to check whether there exists such a composite of bounded degree, and methods are provided to show its nonexistence.

MSC:

12E05 Polynomials in general fields (irreducibility, etc.)
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