Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

Shuichi Otake

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζn)/Q to OQ(ζn) and we get orthogonal decompositions of symmetric Z-bilinear modules OQ(ζn) into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric Zp-bilinear modules Zp⊗ZOQ(ζn) over Zp the ring of p-adic integers.

    Original languageEnglish
    Pages (from-to)258-279
    Number of pages22
    JournalJournal of Number Theory
    Volume134
    DOIs
    Publication statusPublished - 2014 Jan

    Keywords

    • Bezoutian
    • Cyclotomic field
    • Integral trace form
    • Primary
    • Secondary

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Fingerprint Dive into the research topics of 'Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers'. Together they form a unique fingerprint.

  • Cite this