The Factorization of p in Q(a 1/pk) and the Genus Field of Q(a1/n)

William Yslas Vélez

doi:10.3836/tjm/1270134258

The Factorization of p in Q(a ^1/p^k) and the Genus Field of Q(a^1/n)

William Yslas Vélez

Mathematics

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Abstract

Let x^pk-a be irreducible over 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 Q(a^1/pk). As an application of the above we use these results to determine the genus field of Q(a^1/n), where xⁿ-a is irreducible over Q and we make no restrictions on a.

Original language	English (US)
Pages (from-to)	1-19
Number of pages	19
Journal	Tokyo Journal of Mathematics
Volume	11
Issue number	1
DOIs	https://doi.org/10.3836/tjm/1270134258
State	Published - Jun 1988

ASJC Scopus subject areas

General Mathematics

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abstract = "Let xpk-a be irreducible over 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 Q(a1/pk). As an application of the above we use these results to determine the genus field of Q(a1/n), where xn-a is irreducible over Q and we make no restrictions on a.",

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N2 - Let xpk-a be irreducible over 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 Q(a1/pk). As an application of the above we use these results to determine the genus field of Q(a1/n), where xn-a is irreducible over Q and we make no restrictions on a.

AB - Let xpk-a be irreducible over 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 Q(a1/pk). As an application of the above we use these results to determine the genus field of Q(a1/n), where xn-a is irreducible over Q and we make no restrictions on a.

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The Factorization of p in Q(a ^1/p^k) and the Genus Field of Q(a^1/n)

Abstract

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