Abstract: In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial x^p-m(m is p-th powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.

Key words: number ,  field ,  , of ,  Eisenstein ,  type;totally ,  , ramified;prime ,  ideal ,  , factorization, element of Eisenstein type;subfield of degree p