COMPOSITION OF POLYNOMIALS OVER A FIELD

Abstract

This work studies about the composition polynomial f (g(x)) that preserves certain properties of f (x) and g(x). We shall investigate necessary and sufficient conditions of f (x) and g(x) to be f (g(x)) is separable, solvable by radical or split completely. And we find relationship of Galois groups of f (g(x)), f (x) and of g(x).

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