On the factorization of rational primes in cubic cyclotomic number fields. (Q1476432)
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scientific article; zbMATH DE number 2620918
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the factorization of rational primes in cubic cyclotomic number fields. |
scientific article; zbMATH DE number 2620918 |
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On the factorization of rational primes in cubic cyclotomic number fields. (English)
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1913
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Es sei \(p\) eine Primzahl der Form \(6n+1\). Dann enthält der Körper der \(p\)-ten Einheitswurzeln einen \textit{Abel}schen Unterkörper dritten Grades, der durch eine Gleichung der Form \[ y^3-3py-pA=0, \] wo \(4p=A^2+27B^2\) und \(A\equiv 1(\text{mod.} 3)\) ist, gegeben werden kann. Der Verf. studiert die Zerlegung der Primzahlen in diesem kubischen Körper \(k\).
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