Computation of integral bases

J.D. Bauch

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
1 Downloads (Pure)

Abstract

Let A be a Dedekind domain, K the fraction field of A, and f∈. A[. x] a monic irreducible separable polynomial. For a given non-zero prime ideal p of A we present in this paper a new characterization of a p-integral basis of the extension of K determined by f. This characterization yields in an algorithm to compute p-integral bases, which is based on the use of simple multipliers that can be constructed with the data that occurs along the flow of the Montes Algorithm. Our construction of a p-integral basis is significantly faster than the similar approach from [8] and provides in many cases a priori a triangular basis.

Original languageEnglish
Pages (from-to)382-407
Number of pages26
JournalJournal of Number Theory
Volume165
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Dedekind domain
  • Maximal order
  • Montes algorithm
  • P-Integral bases

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