Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496491 | Journal of Number Theory | 2005 | 30 Pages |
Abstract
In analogy to the Kummer theory such a coset gives rise to the definition of an order OËP in an algebra MP and to an associated order A defined below by its local components. These objects naturally come into play in the Galois module structure of rings of integers in ray class fields over K. It is the aim of this article to construct global generators both for OËP and A as algebras over the ring of integers of L. For the convenience of the reader we also include from (J. Number Theory 77 (1999) 97) a simple construction of Galois generators for OËP over A. We thereby show that these generators also fit in the setting of this article that is more general than in [Sch4]. The main results in Theorems 3, 6 and 7 are obtained assuming the base field L to contain “enough” torsion points of E.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Reinhard Schertz,