AbstractLet p and l be odd primes. As a consequence of a work of Brinkhuis (Math. Ann. 264 (1983), 537–543) one can prove that if p ≡ 1 mod l2 the ring of integers of the pth cyclotomic field has no normal integral bases over the ring of integers of the subfield of relative degree l. This method does not work when the congruence is only p ≡ 1 mod l. In this article we study this last case and prove that if (p − 1)l is not a power of two there is no relative integral bases
AbstractLet K be any number field, and let E be a quadratic or a biquadratic extension of K. We give...
Let L be a quartic number field with a quadratic subfield K. In 1986 Kawamoto gave a necessary and s...
AbstractFor any natural number g ≥ 2, and for any odd prime p not dividing g, we give an explicit ex...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractLet K/Q be a cyclic extension of degree l. Let ZK be the ring of integers of K. We say that ...
AbstractLet p be an odd prime number, K an imaginary abelian field with ζp∈K×, and K∞/K the cyclotom...
AbstractLet K be an algebraic function field of one variable over a finite field of characteristic p...
AbstractLet K/F be a Kummer cyclic extension of number fields. In the case when the degree is a prim...
AbstractLet p be an odd prime and let η be a unit of the ring of integers of the pnth cyclotomic fie...
Abstract. Let K be an abelian field whose Galois group is 2-elementary abelian over the rationals Q....
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
AbstractLet ζ be a primitive 2mth root of unity. We prove that Z[α]=Z[ζ] if and only if α=n±ζi for s...
Let p 3 be a prime number, F be a number field with ζp / ∈ F×, and K = F (ζp). In a previous paper,...
Let $K/F$ be a Kummer cyclic extension of number fields. In the case when the degree is a prime n...
AbstractLet K be any number field, and let E be a quadratic or a biquadratic extension of K. We give...
Let L be a quartic number field with a quadratic subfield K. In 1986 Kawamoto gave a necessary and s...
AbstractFor any natural number g ≥ 2, and for any odd prime p not dividing g, we give an explicit ex...
AbstractThe current paper considers the question of power bases in the cyclotomic number field Q(ζ),...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractLet K/Q be a cyclic extension of degree l. Let ZK be the ring of integers of K. We say that ...
AbstractLet p be an odd prime number, K an imaginary abelian field with ζp∈K×, and K∞/K the cyclotom...
AbstractLet K be an algebraic function field of one variable over a finite field of characteristic p...
AbstractLet K/F be a Kummer cyclic extension of number fields. In the case when the degree is a prim...
AbstractLet p be an odd prime and let η be a unit of the ring of integers of the pnth cyclotomic fie...
Abstract. Let K be an abelian field whose Galois group is 2-elementary abelian over the rationals Q....
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
AbstractLet ζ be a primitive 2mth root of unity. We prove that Z[α]=Z[ζ] if and only if α=n±ζi for s...
Let p 3 be a prime number, F be a number field with ζp / ∈ F×, and K = F (ζp). In a previous paper,...
Let $K/F$ be a Kummer cyclic extension of number fields. In the case when the degree is a prime n...
AbstractLet K be any number field, and let E be a quadratic or a biquadratic extension of K. We give...
Let L be a quartic number field with a quadratic subfield K. In 1986 Kawamoto gave a necessary and s...
AbstractFor any natural number g ≥ 2, and for any odd prime p not dividing g, we give an explicit ex...
DOI
Add to ORKG