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 xm − μ irreducible over F. If m is a prime and ζm ϵ F, then the ideal decomposition of (Formula Precented) in F(μ1/m) has been described by Hensel. If m = lt, l a prime and (l, P) = 1, then the decomposition of (Formula Precented) in F(μ1/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(ζp) and F(μ1/p), where (Formula Precented) ⊃(p).
|Original language||English (US)|
|Number of pages||12|
|Journal||Pacific Journal of Mathematics|
|State||Published - 1978|
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