Prime ideal decomposition in F(μ^1/p)

Let F be a finite extension of the field of rational numbers (Formula Precented), a prime ideal in the ring of algebraic integers in F, and x^m − μ irreducible over F. If m is a prime and ζ_m ϵ F, then the ideal decomposition of (Formula Precented) in F(μ^1/m) has been described by Hensel. If m = l^t, l a prime and (l, P) = 1, then the decomposition of (Formula Precented) in F(μ^1/lt) was obtained by Mann and Velez, with no restriction on roots of unity. In this paper we describe the decomposition of (Formula Precented) in the fields F(ζ_p) and F(μ^1/p), where (Formula Precented) ⊃(p).