关于复合多项式不可约因式的次数

On the Degrees of Irreducible Factors of Composite Polynomials

设m ,n是正整数 ,g(x) ,h(x)分别是数域F上的m ,n次多项式 ;又设f(x) =g(h(x) ) .证明了如果g(x)在F上不可约 ,则f(x)

Let F be a number field.Let g(x) and h(x) be polynomials over F with the degrees m and n respectively.In this paper we prove that if g(x) is irreducible over F ,then the degrees of irreducible factors of the composite polynomial g(h(x)) over F do not less than m .