The Decomposition of Primes in Torsion Point Fields
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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. eBook.

Lieferung aus: Deutschland, Lagernd.
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. Soft cover.

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Adelmann: Decomposition 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. 22.05.2001, Taschenbuch.

Von Händler/Antiquariat, Rheinberg-Buch [53870650], Bergisch Gladbach, NRW, Germany.
Neuware - 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. 142 pp. Englisch.

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Decomposition of Primes in Torsion Point Fields: 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. Englisch, Ebook.

Lieferung aus: Deutschland, Versandkostenfrei.
Rhein-Team Lörrach, [3332481].
Neuware - 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. -, Taschenbuch.

Lieferung aus: Deutschland, Versandkostenfrei.
buchZ AG, [3859792].
Neuware - 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. Taschenbuch.

Lieferung aus: Vereinigte Staaten von Amerika, Lagernd, zzgl. Versandkosten.
We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases.

Lieferung aus: Vereinigte Staaten von Amerika, zzgl. Versandkosten, Free Shipping on eligible orders over $25.
We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases.