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Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and $a_{}$ any generator of the principal ideal ${}^{\ell }$. We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates $Gal(K\left(\sqrt[\ell ]{a_{}}\right)/K)$ for every choice of $a_{}$. We then show that becomes principal in L if and only if every reciprocal prime is not a norm inside...