Subsemigroups of Finitely Generated Groups with Divisor-Theory.
The ring of integers of an abelian number field.
Note on the Galois module structure of quadratic extensions
In this note we will determine the associated order of relative extensions of algebraic number fields, which are cyclic of prime order p, assuming that the ground field is linearly disjoint to the pth cyclotomic field, . For quadratic extensions we will furthermore characterize when the ring of integers of the extension field is free over the associated order. All our proofs are quite elementary. As an application, we will determine the Galois module structure of .
Relative Galois module structure of integers of local abelian fields
Thue equations over algebraic function fields
Parametrized solutions of Diophantine equations
Power series and zeroes of trinomial equations.
Power series and zeroes of trinomial equations. (Summary).
Relative Galois module structure of integers of abelian fields
Let be an extension of algebraic number fields, where is abelian over . In this paper we give an explicit description of the associated order of this extension when is a cyclotomic field, and prove that , the ring of integers of , is then isomorphic to . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that is the maximal order if is a cyclic and totally wildly ramified extension which is linearly disjoint to , where is the conductor of .
On covers of abelian groups by cosets
Page 1