On a certain type of characters of the idèle-class group of an algebraic number-field

1979 ◽  
pp. 777-783
Author(s):  
André Weil
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Class Group ◽  
Algebraic Number Field

scholarly journals A PRECISE RESULT ON THE ARITHMETIC OF NON-PRINCIPAL ORDERS IN ALGEBRAIC NUMBER FIELDS

2012 ◽  
Vol 11 (05) ◽  
pp. 1250087 ◽  
Author(s):  
ANDREAS PHILIPP
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Theoretical Approach ◽  
Class Group ◽  
Algebraic Number Field ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
Precise Result ◽  
Principal Order

Let R be an order in an algebraic number field. If R is a principal order, then many explicit results on its arithmetic are available. Among others, R is half-factorial if and only if the class group of R has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

scholarly journals A generalization of Hubert’s Theorem 94

1984 ◽  
Vol 96 ◽  
pp. 83-94 ◽  
Author(s):  
Katsuya Miyake
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Class Group ◽  
Algebraic Number Field ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Finite Degree ◽  
Class Field ◽  
The Absolute

Let k be an algebraic number field of finite degree. We denote the absolute class field of k by and the absolute ideal class group of k by Cl(k).

Conjugacy Classes and Class Number

Integers ◽  
2009 ◽  
Vol 9 (4) ◽  
Author(s):  
Ashay Burungale
Keyword(s):  
Number Field ◽  
Characteristic Polynomial ◽  
Algebraic Number ◽  
Class Number ◽  
Class Group ◽  
Algebraic Number Field ◽  
Conjugacy Classes ◽  
Integral Matrices

AbstractIt is shown that the conjugacy classes of integral matrices with a given irreducible characteristic polynomial is in bijection with the class group of a corresponding order in an algebraic number field.

scholarly journals On the rank of the first radical layer of a p-class group of an algebraic number field

1999 ◽  
Vol 156 ◽  
pp. 85-108
Author(s):  
Hiroshi Yamashita
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Sylow Subgroup ◽  
Class Group ◽  
Cyclotomic Field ◽  
Artinian Ring ◽  
Algebraic Number Field ◽  
Central Extensions ◽  
Genus Field ◽  
Global And Local

Let p be a prime number. Let M be a finite Galois extension of a finite algebraic number field k. Suppose that M contains a primitive pth root of unity and that the p-Sylow subgroup of the Galois group G = Gal(M/k) is normal. Let K be the intermediate field corresponding to the p-Sylow subgroup. Let = Gal(K/k). The p-class group C of M is a module over the group ring ZpG, where Zp is the ring of p-adic integers. Let J be the Jacobson radical of ZpG. C/JC is a module over a semisimple artinian ring Fp. We study multiplicity of an irreducible representation Φ apperaring in C/JC and prove a formula giving this multiplicity partially. As application to this formula, we study a cyclotomic field M such that the minus part of C is cyclic as a ZpG-module and a CM-field M such that the plus part of C vanishes for odd p.To show the formula, we apply theory of central extensions of algebraic number field and study global and local Kummer duality between the genus group and the Kummer radical for the genus field with respect to M/K.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

scholarly journals The trace-form of an algebraic number field

1973 ◽  
Vol 5 (5) ◽  
pp. 379-384 ◽  
Author(s):  
Donald Maurer
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Trace Form
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