If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
Let $K$ be a cyclic totally real number field of odd degree over $\mathbb{Q}$ with odd class number,...
summary:If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prim...
summary:If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prim...
Due to a theorem of Dedekind, factoring ideals generated by prime numbers in number fields is easily...
summary:Let $K$ be a number field defined by an irreducible polynomial $F(X)\in \mathbb Z[X]$ and $\...
The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicit...
The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicit...
Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric ...
summary:Let $K$ be a number field defined by an irreducible polynomial $F(X)\in \mathbb Z[X]$ and $\...
AbstractA p-adic method for the constructive factorization of monic polynomials over a dedekind ring...
AbstractFor a given positive integer m and an algebraic number field K necessary and sufficient cond...
It is often taken it for granted that all positive whole numbers except 0 and 1 can be factored uniq...
One branch of number theory is ramification theory, which studies the behavior of primes in L/K, whe...
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
Let $K$ be a cyclic totally real number field of odd degree over $\mathbb{Q}$ with odd class number,...
summary:If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prim...
summary:If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prim...
Due to a theorem of Dedekind, factoring ideals generated by prime numbers in number fields is easily...
summary:Let $K$ be a number field defined by an irreducible polynomial $F(X)\in \mathbb Z[X]$ and $\...
The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicit...
The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicit...
Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric ...
summary:Let $K$ be a number field defined by an irreducible polynomial $F(X)\in \mathbb Z[X]$ and $\...
AbstractA p-adic method for the constructive factorization of monic polynomials over a dedekind ring...
AbstractFor a given positive integer m and an algebraic number field K necessary and sufficient cond...
It is often taken it for granted that all positive whole numbers except 0 and 1 can be factored uniq...
One branch of number theory is ramification theory, which studies the behavior of primes in L/K, whe...
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
Let $K$ be a cyclic totally real number field of odd degree over $\mathbb{Q}$ with odd class number,...