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

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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.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalTokyo Journal of Mathematics
Volume11
Issue number1
DOIs
Publication statusPublished - 1988

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ASJC Scopus subject areas

  • Mathematics(all)

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