Prime Splitting and Common Index Divisors in Radical Extensions
| Autor: | Smith, Hanson |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We explicitly describe the splitting of odd integral primes in the radical extension $\mathbb{Q}(\sqrt[n]{a})$, where $x^n-a$ is an irreducible polynomial in $\mathbb{Z}[x]$. Our motivation is to classify common index divisors, the primes whose splitting prevents the existence of a power integral basis for the ring of integers of $\mathbb{Q}(\sqrt[n]{a})$. Among other results, we show that if $p$ is such a prime, even or otherwise, then $p\mid n$. Comment: 23 pages. Comments welcome! |
| Databáze: | arXiv |
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