The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it i...The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.展开更多
Assume that K is a number field, L<sub>i</sub>=K(D<sub>i</sub><sup>1/2</sup>)（i=1, 2）, where D<sub>1</sub>, D<sub>2</sub>∈K\K<sup>2</sup> and ...Assume that K is a number field, L<sub>i</sub>=K(D<sub>i</sub><sup>1/2</sup>)（i=1, 2）, where D<sub>1</sub>, D<sub>2</sub>∈K\K<sup>2</sup> and L<sub>1</sub>≠L<sub>2</sub>. Let L=L<sub>1</sub>L<sub>2</sub>. It is well-known that L/K has three intermediate subfields of degree 2, which are L<sub>1</sub>, L<sub>2</sub> and L3=K(D<sub>1</sub>D<sub>2</sub><sup>1/2</sup>).展开更多
The purpose of this paper is to discuss the property of the primes splitting completely in the finite extension L of number field K. If K is a number field, we denote by O_K the integer ring of K.
Quartic unramified Abelian extension fields of a class of cubic cyclic fields are given and the Hilbert class field of a cubic cyclic field with discriminant 607~2 iS obtained.
According to the idea of class field theory, the possible absolutely normal number fieldsare restricted in nature by the arithmetical properties of rational number field .Becausethe fundamental arithmetical property o...According to the idea of class field theory, the possible absolutely normal number fieldsare restricted in nature by the arithmetical properties of rational number field .Becausethe fundamental arithmetical property of is the distributive law of the prime numbers,展开更多
文摘The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.
基金Project supported by the National Natural Science Foundation of China.
文摘Assume that K is a number field, L<sub>i</sub>=K(D<sub>i</sub><sup>1/2</sup>)（i=1, 2）, where D<sub>1</sub>, D<sub>2</sub>∈K\K<sup>2</sup> and L<sub>1</sub>≠L<sub>2</sub>. Let L=L<sub>1</sub>L<sub>2</sub>. It is well-known that L/K has three intermediate subfields of degree 2, which are L<sub>1</sub>, L<sub>2</sub> and L3=K(D<sub>1</sub>D<sub>2</sub><sup>1/2</sup>).
文摘The purpose of this paper is to discuss the property of the primes splitting completely in the finite extension L of number field K. If K is a number field, we denote by O_K the integer ring of K.
文摘Quartic unramified Abelian extension fields of a class of cubic cyclic fields are given and the Hilbert class field of a cubic cyclic field with discriminant 607~2 iS obtained.
文摘According to the idea of class field theory, the possible absolutely normal number fieldsare restricted in nature by the arithmetical properties of rational number field .Becausethe fundamental arithmetical property of is the distributive law of the prime numbers,
