Skip to main content
SpringerLink
Log in
Book cover

The Decomposition of Primes in Torsion Point Fields

  • Book
  • © 2001

Overview

Editors:
  1. Clemens Adelmann

    1. Institute of Applied Mathematics Dept. of Applied Algebra, Technical University Braunschweig, Braunschweig, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1761)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages I-V
    Download chapter PDF

  2. Introduction

    Pages 1-4

  3. Decomposition Laws

    Pages 5-24

  4. Elliptic Curves

    Pages 25-39

  5. Elliptic Modular Curves

    Pages 41-58

  6. Torsion Point Fields

    Pages 59-86

  7. Invariants and Resolvent Polynomials

    Pages 87-106

  8. Back Matter

    Pages 107-140
    Download chapter PDF
Back to top

Keywords

About this book

It is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the considered number ?eld. By examining the behaviouroftheprimeidealswhenembeddedintheextension?eld,su?cient information should be collected to distinguish the given extension from all other possible extension ?elds. The ring of integers O of an algebraic number ?eld k is a Dedekind ring. k Any non-zero ideal in O possesses therefore a decomposition into a product k of prime ideals in O which is unique up to permutations of the factors. This k decomposition generalizes the prime factor decomposition of numbers in Z Z. In order to keep the uniqueness of the factors, view has to be changed from elements of O to ideals of O . k k Given an extension K/k of algebraic number ?elds and a prime ideal p of O , the decomposition law of K/k describes the product decomposition of k the ideal generated by p in O and names its characteristic quantities, i. e. K the number of di?erent prime ideal factors, their respective inertial degrees, and their respective rami?cation indices. Whenlookingatdecompositionlaws,weshouldinitiallyrestrictourselves to Galois extensions. This special case already o?ers quite a few di?culties.

Editors and Affiliations

  • Institute of Applied Mathematics Dept. of Applied Algebra, Technical University Braunschweig, Braunschweig, Germany

    Clemens Adelmann

Bibliographic Information

  • Book Title: The Decomposition of Primes in Torsion Point Fields

  • Editors: Clemens Adelmann

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b80624

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Softcover ISBN: 978-3-540-42035-4Published: 22 May 2001

  • eBook ISBN: 978-3-540-44949-2Published: 11 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 148

  • Topics: Number Theory, Algebraic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation