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June 1988 The Factorization of $p$ in $\mathbf{Q}(a^{1/p^k})$ and the Genus Field of $\mathbf{Q}(a^{1/n})$
William Yslas VÉLEZ
Tokyo J. Math. 11(1): 1-19 (June 1988). DOI: 10.3836/tjm/1270134258

Abstract

Let $x^{p^k}-a$ be irreducible over $\mathbf{Q}$. The first part of this paper is to explicitly give the decomposition rules for the factorization of $p$ in the ring of integers of $\mathbf{Q}(a^{1/p^k})$.

As an application of the above we use these results to determine the genus field of $\mathbf{Q}(a^{1/n})$, where $x^n-a$ is irreducible over $\mathbf{Q}$ and we make no restrictions on $a$.

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William Yslas VÉLEZ. "The Factorization of $p$ in $\mathbf{Q}(a^{1/p^k})$ and the Genus Field of $\mathbf{Q}(a^{1/n})$." Tokyo J. Math. 11 (1) 1 - 19, June 1988. https://doi.org/10.3836/tjm/1270134258

Information

Published: June 1988
First available in Project Euclid: 1 April 2010

zbMATH: 0664.12003
MathSciNet: MR947943
Digital Object Identifier: 10.3836/tjm/1270134258

Rights: Copyright © 1988 Publication Committee for the Tokyo Journal of Mathematics

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Vol.11 • No. 1 • June 1988
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