有理数域上分圆多项式的不可约性

The Irreducibility of Cyclotomic Polynomials on Rational Number Fields

本文探讨了有理数域上分圆多项式的性质和推论,给出了n阶分圆多项式与本原n次单位根的最小多项式之间的关系,得到了n阶分圆多项式在有理数域上是不可约的结论,为有理数域上不可约多项式理论的完善和应用提供一些理论依据.

The properties and inferences of cyclotomic polynomials on rational number fields are discussed.The relation between n-order cyclotomic polynomials and the minimum polynomials of the unit roots of primitive n-degree are given.The conclusion that n-order cyclotomic polynomials are irreducible in rational number fields are obtained,which provides a basis for the perfection and application of the theory of irreducible polynomials on rational number fields.