On a theorem of Ore (Q1184186)

The paper gives a generalization of a theorem of \textit{Ø. Ore} [Math. Ann. 99, 84--117 (1928; JFM 54.0191.02)] on the prime ideal decomposition of the rational primes in a number field \(K\). The authors use Newton's polygon techniques, as Ore and they give a much weaker condition, under which the method is still applicable. An effective criterion is formulated to decide if the condition is satisfied. The algorithm reduces the problem of prime ideal decomposition to polynomial factorizations over finite fields. The paper includes also a survey on the classical results of Kummer, Dedekind and on the work of Ore in this field.