Decomposition Of Prime Ideal (P) In Q(μ^1/19)

The decomposition of prime ideal has been very important thesis in the algebraic number theory.The class field theory shows that how to determine the issue with all the base of F is closely related to the extension of Galois field. So many researchers studied lots of the issue of decomposition of prime ideal in the internal and external.Let R be the field of rational numbers and? be its valuation of rank 1 non-trivial and non-archimedean. Let R be the valuation ring with respect to? . Let P be the prime ideal. In the paper x 19-μ(μ∈R)is a unique monic irreducible polynomial in rational number fieldsQ .19 is coprime with the character of F. If K/Q is rank of 19 Galois extension, we have discussed the question of decomposition of prime ideal (p )in Q(μ1/19)in the paper. We give a complete proof that the decomposition of the form of prime ideal (p )in Q(μ1/19)is decided by the extension of (p )in Q (ζ19)and the decomposition form of the extension in Q (μ1/19).