## 8 Citations

### P\'olya-Ostrowski Group and Unit Index in Real Biquadratic Fields

- Mathematics
- 2021

Pólya group of a Galois number field K is the subgroup of the ideal class group of K generated by all strongly ambiguous ideal classes. In this paper, using Galois cohomology and some results in [14,…

### Totally real bi-quadratic fields with large Pólya groups

- MathematicsResearch in Number Theory
- 2022

For an algebraic number field K with ring of integers OK , an important subgroup of the ideal class group ClK is the Pólya group, denoted by Po(K), which measures the failure of the OK -module…

### Ostrowski quotients for finite extensions of number fields

- Mathematics
- 2021

. For L/K a ﬁnite Galois extension of number ﬁelds, the relative P´olya group Po( L/K ) coincides with the group of strongly ambiguous ideal classes in L/K . In this paper, using a well known exact…

### Pre-Pólya group in even dihedral extensions of ℚ

- Mathematics
- 2020

Investigating on Pólya groups [P. J. Cahen and J. L. Chabert Integer-Valued Polynomials, Mathematical Surveys and Monographs, Vol. 48 (American Mathematical Society, Providence, 1997)] in non-Galois…

### The analogue of the BRZ exact sequence for Tate-Shafarevich Groups

- Mathematics
- 2022

We find an exact sequence in term of Tate-Shafarevich groups (assuming being finite) X(E/K) and X(E/L) of elliptic curve E over a finite Galois extension L/K of number fields. This is the analogue of…

### Existence of relative integral basis over quadratic fields and Pólya property

- Mathematics
- 2021

For $$L/K$$ L / K a finite extension of algebraic number fields, L may or may not have a relative integral basis over K. We show the existence of relative integral basis of a biquadratic field…

## References

SHOWING 1-10 OF 32 REFERENCES

### Pólya S3-extensions of ℚ

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2019

Abstract A number field K with a ring of integers 𝒪K is called a Pólya field, if the 𝒪K-module of integer-valued polynomials on 𝒪K has a regular basis, or equivalently all its Bhargava factorial…

### Some non-Pólya biquadratic fields with low ramification

- Mathematics
- 2017

Polya fields are fields with principal Bhargava factorial ideals, and as a generalization of class number one number fields, their classification might be of interest to number theorists. It is known…

### Class Number and Ramification in Number Fields

- MathematicsNagoya Mathematical Journal
- 1963

In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk , the class number of K. The…

### Class Field Theory

- Mathematics
- 2008

A Brief Review.- Dirichlet#x2019 s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Id#x00E8 lic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and…

### Integer valued polynomials over a number field

- Mathematics
- 1982

A number field is called a Pólya field if the module of integer valued polynomials over that field is generated by (fi)i=0∞ over the ring of integers, with deg(fi)=i, i=0, 1, 2,... In this paper…