The Decomposition of Primes in Torsion Point Fields (Record no. 11441)
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fixed length control field | 03430nam a22004815i 4500 |
001 - CONTROL NUMBER | |
control field | 978-3-540-44949-2 |
003 - CONTROL NUMBER IDENTIFIER | |
control field | DE-He213 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20190213151646.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
fixed length control field | cr nn 008mamaa |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 121227s2001 gw | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9783540449492 |
-- | 978-3-540-44949-2 |
024 7# - OTHER STANDARD IDENTIFIER | |
Standard number or code | 10.1007/b80624 |
Source of number or code | doi |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA241-247.5 |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBH |
Source | bicssc |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | MAT022000 |
Source | bisacsh |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBH |
Source | thema |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 512.7 |
Edition number | 23 |
245 14 - TITLE STATEMENT | |
Title | The Decomposition of Primes in Torsion Point Fields |
Medium | [electronic resource] / |
Statement of responsibility, etc | edited by Clemens Adelmann. |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg, |
-- | 2001. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | VIII, 148 p. |
Other physical details | online resource. |
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-- | text |
-- | txt |
-- | rdacontent |
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-- | computer |
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-- | rdamedia |
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-- | online resource |
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-- | rdacarrier |
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-- | text file |
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-- | rda |
490 1# - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics, |
International Standard Serial Number | 0075-8434 ; |
Volume number/sequential designation | 1761 |
505 0# - FORMATTED CONTENTS NOTE | |
Formatted contents note | Introduction -- Decomposition laws -- Elliptic curves -- Elliptic modular curves -- Torsion point fields -- Invariants and resolvent polynomials -- Appendix: Invariants of elliptic modular curves; L-series coefficients a p; Fully decomposed prime numbers; Resolvent polynomials; Free resolution of the invariant algebra. |
520 ## - SUMMARY, ETC. | |
Summary, etc | 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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Number theory. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Geometry, algebraic. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Number Theory. |
-- | http://scigraph.springernature.com/things/product-market-codes/M25001 |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Algebraic Geometry. |
-- | http://scigraph.springernature.com/things/product-market-codes/M11019 |
700 1# - ADDED ENTRY--PERSONAL NAME | |
Personal name | Adelmann, Clemens. |
Relator term | editor. |
Relator code | edt |
-- | http://id.loc.gov/vocabulary/relators/edt |
710 2# - ADDED ENTRY--CORPORATE NAME | |
Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY | |
Title | Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783662185209 |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783540420354 |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
Uniform title | Lecture Notes in Mathematics, |
-- | 0075-8434 ; |
Volume number/sequential designation | 1761 |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | https://doi.org/10.1007/b80624 |
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-- | ZDB-2-LNM |
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