Prime ideal decomposition in {Mathematical expression}

Henry B. Mann, William Yslas Vélez

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let F be an algebraic number field and μ∈F such that xm-μ is irreducible, where m is an integer. Let {Mathematical expression} be a prime ideal in F with {Mathematical expression}. The prime decomposition of {Mathematical expression} in {Mathematical expression} is explicitly obtained in the following cases. Case 1: {Mathematical expression}, (a,m) = 1 (where {Mathematical expression} means {Mathematical expression}, ς ≢ 0 {Mathematical expression}). Case 2:m ≡lt, where l is a prime and l ≢ 0 {Mathematical expression}. Case 3:m ≢ 0 {Mathematical expression} and every prime that divides m also divides pf-1. It is not assumed that the vth roots of unity are in F for any v ≠ 2.

Original languageEnglish (US)
Pages (from-to)131-139
Number of pages9
JournalMonatshefte für Mathematik
Volume81
Issue number2
DOIs
StatePublished - Jun 1 1976

ASJC Scopus subject areas

  • Mathematics(all)

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